Trigonometry in Real Life

Growing with Applied Mathematics Experiences (G.A.M.E)

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Trigonometry in Real Life

Trigonometry in Real Life

Applications in arts

Applications in music

Applications in medicine

Applications in Geography

Applications in engineering

Applications in Physics

Applications in navigation

Applications in architecture

Applications in astronomy

Arina B.Gaudeamus High School, Moldova

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Applications in astronomy

Zlata D.Gaudeamus High School, Moldova

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Applications in astronomy

Nicoli M.Gaudeamus High School, Moldova

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Applications in astronomy

Daniel P.Gaudeamus High School, Moldova

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Applications in astronomy

Efsa baruthane Baruthane secondary school Turkey

Subtitle

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Birunî used trigonometry to calculate the radius of the Earth. First, to measure the height of a mountain rising on a flat plain, he measured the angles between two points with known distances between them and the mountain's peak. From these data, he calculated the height of the mountain through trigonometric calculations.

Applications in astronomy

Mădălina B.Gaudeamus High School, Moldova

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Applications in astronomy

Cristian-Patriciu, Gaudeamus High School, Moldova

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Applications in astronomy

Gaudeamus High School, Moldova

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Applications in astronomy

Mariela, Gaudeamus High School, Moldova

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Applications in astronomy

Gaudeamus High School, Moldova

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Applications in astronomy

Gaudeamus High School, Moldova

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Applications in astronomy

Vlad T.Gaudeamus High School, Moldova

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Applications in astronomy

Vlad V.Gaudeamus High School, Moldova

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Applications in astronomy

Marius R.Gaudeamus High School, Moldova

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Applications in astronomy

Evghenii, Gaudeamus High School, Moldova

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Applications in astronomy

Mihai N.Gaudeamus High School, Moldova

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Applications in astronomy

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Louise, Cité Scolaire Brocéliande France

Applications in astronomy

MeikoCité Scolaire Brocéliande France

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Applications in astronomy

Léopold, Cité Scolaire Brocéliande France

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Applications in astronomy

Cantacuzino Castle has a great architectural, historical, documentary and artistic value. The castle building was completed in 1911, being made according to the plans of the architect Grigore Cerchez, a prominent figure of the Neo-Romanian current, at the request of Prince Gheorghe Grigore Cantacuzino

Jean Monnet High School, Romania

The ceiling

Cantacuzino Castle -Bușteni - Romania

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Applications in architecture

Modeling in GeoGebra, using the sine function

Ceiling detail

Jean Monnet High School, Romania

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Applications in architecture

By Cmichel67 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=93168755

Crooked Street

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Applications in architecture

Problem

Construct a regular dodecagon ABC...KL. Construct the regular hexagons ACEGIK and BDFHJL. Intersecting the 2 hexagons, the star polygon with 24 sides is formed. Calculate the area of a regular star polygon with 24 sides, knowing the radius of the circle circumscribing the polygon ABCDEF...KL of 2 units. Calculate the blue area in the attached figure, bounded by the circle with radius 1 unit and the star polygon.

Inspiration - mosaic Romanian Athenaeum-Bucharest

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De la fusion-of-horizons - Flickr, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=21814139

Applications in architecture

Solution

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Applications in architecture

Distance with Google Map :

Bodysgallen Hall is a manor house in Conwy county borough, north Wales, near the village of Llanrhos. Since 2008 the house has been owned by The National Trust. It is a Grade I listed building, currently used as a hotel. This listed historical building derives primarily from the 17th century. Bodysgallen was constructed as a tower house in the Middle Ages to serve as defensive support for nearby Conwy Castle.

One of the gardens has a circular shape with a diameter of 10m. It is divided into 10 equal parcels, cultivated alternately with lavender and dwarf shrubs. in the center there is a circular area with a diameter of 2m with grass.

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Bodysgallen Hall, UK

https://www.bodysgallen.com/

Applications in architecture

1. Find out the area of the area cultivated with lavender.2. The surface of the garden will be restricted to the regular decagon ABCDEFGHIJ. Calculate its area.

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Applications in architecture

Maria A.Gaudeamus High School, Moldova

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Applications in architecture

Arina B.Gaudeamus High School, Moldova

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Applications in architecture

Zlata D.Gaudeamus High School, Moldova

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Applications in architecture

Mariela D.Gaudeamus High School, Moldova

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Applications in architecture

Macovei N.Gaudeamus High School, Moldova

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Applications in architecture

Daniel P.Gaudeamus High School, Moldova

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Applications in architecture

Angelina S.Gaudeamus High School, Moldova

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Applications in architecture

Elif Ayse Baruthane secondary School Turkey

One of the most common architectural uses for trigonometry is to determine the height of a structure. For example, architects can use the tangent function to calculate the height of the building if they know the distance from the structure and the angle between their eyes and the top of the building; clinometers can help you measure these angles.

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Applications in architecture

BEYZA,BARUTHANE SECONDARY SCHOOL,TURKEY

A clear example of the use of trigonometry in architecture is in the Egyptian pyramids.

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Applications in architecture

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Ogan, Baruthane Secondary School,Turkey

Applications in architecture

Briana T..Gaudeamus High School, Moldova

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Applications in architecture

Vlad, Gaudeamus High School, Moldova

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Applications in architecture

Gaudeamus High School, Moldova

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Applications in architecture

Gaudeamus High School, Moldova

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Applications in architecture

Gaudeamus High School, Moldova

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Applications in architecture

Mădălina G.Gaudeamus High School, Moldova

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Applications in architecture

Gaudeamus High School, Moldova

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Applications in architecture

Gaudeamus High School, Moldova

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Applications in architecture

Vlad V.Gaudeamus High School, Moldova

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Applications in architecture

Evghenii.Gaudeamus High School, Moldova

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Applications in architecture

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Applications in architecture

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Applications in architecture

to be followed next page...

Broceliande team 1ereFrance

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Applications in architecture

Part 2

Broceliande team 1ereFrance

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Applications in architecture

AlwenaBroceliande France

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Applications in architecture

CélestinBroceliande France

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Applications in architecture

Arina B.Gaudeamus High School, Moldova

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Applications in navigation

Arina B.Gaudeamus High School, Moldova

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Applications in navigation

Daniel P.Gaudeamus High School, Moldova

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Applications in navigation

Tunay Baruthane Secondary School

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Applications in navigation

.Gaudeamus High School, Moldova

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Applications in navigation

Zlata, Gaudeamus High School, Moldova

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Applications in navigation

Cristian-Patriciu.Gaudeamus High School, Moldova

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Applications in navigation

Mariela, Gaudeamus High School, Moldova

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Applications in navigation

Mădălina GGaudeamus High School, Moldova

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Applications in navigation

Gaudeamus High School, Moldova

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Applications in navigation

Briana.Gaudeamus High School, Moldova

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Applications in navigation

Gaudeamus High School, Moldova

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Applications in navigation

Vlad T.Gaudeamus High School, Moldova

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Applications in navigation

Gaudeamus High School, Moldova

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Applications in navigation

Dragoș.Gaudeamus High School, Moldova

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Applications in navigation

Evghenii.Gaudeamus High School, Moldova

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Applications in navigation

Marius.Gaudeamus High School, Moldova

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Applications in navigation

Mihai NGaudeamus High School, Moldova

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Applications in navigation

Sabina N.Gaudeamus High School, Moldova

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Applications in navigation

Jeanne Brocéliande high school France

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Applications in navigation

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Applications in navigation

Jean Monnet High School

A - Victory Square B - Charles de Gaulle Square C - Arch of TriumphAB=1.6 kmAC=1.8BC=0.7Find A

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Applications in Geography

Florentina, Jean Monnet High School

A - Victory Square B - Charles de Gaulle Square C - Arch of TriumphAB=1.6 kmAC=1.8BC=0.7Find angle A.

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Applications in Geography

Daniel P.Gaudeamus High School, Moldova

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Applications in Geography

Briana T.Gaudeamus High School, Moldova

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Applications in Geography

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BERA, BARUTHANE SECONDARY SCHOOL,TURKEY

In geography, trigonometry is used to calculate distances on a map.

Applications in Geography

Mădălina B.Gaudeamus High School, Moldova

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Applications in Geography

Cristian, Gaudeamus High School, Moldova

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Applications in Geography

Gaudeamus High School, Moldova

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Applications in Geography

Mădălina G.Gaudeamus High School, Moldova

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Applications in Geography

Gaudeamus High School, Moldova

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Applications in Geography

Gaudeamus High School, Moldova

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Applications in Geography

Vlad T.Gaudeamus High School, Moldova

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Applications in Geography

Vlad V.Gaudeamus High School, Moldova

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Applications in Geography

Mariela.Gaudeamus High School, Moldova

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Applications in Geography

Dragoș.Gaudeamus High School, Moldova

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Applications in Geography

MariusGaudeamus High School, Moldova

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Applications in Geography

Sabina N.Gaudeamus High School, Moldova

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Applications in Geography

Mihai N.Gaudeamus High School, Moldova

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Applications in Geography

AmbreCité Scolaire Brocéliande France

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Applications in Geography

Instruments for measuring angles

https://www.pngwing.com/en/free-png-phhpx/download

Denisa, Jean Monnet High School

https://ro.wikipedia.org/wiki/Teodolit

Theodolite is an instrument for measuring angles, being used in geodesy, topography, construction, etc. The measurements are made with the theodolite fixed on a tripod. It is perfectly adjusted horizontally with the help of air bubble levels. The instrument is equipped with a scope with a graduated eyepiece with the help of which the engineer can precisely aim at points on the field.

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Applications in engineering

Matei, Jean Monnet High School

Determining the height of a tower

Applications in engineering

The height of a tree - experiment

Teofil, Matei, Andrei, Sofia, Mara -Jean Monnet High School

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Applications in engineering

Teofil, Jean Monnet High School

AB - the length of the tree's shadow is measured AD - the bat shadow is measured CD - the length of the stick is measured 1) to find the height of the tree.2) to find the measure of the angle under which the tree is seen: EAB

The height of a tree

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Applications in engineering

The height of a tower

Irina, Jean Monnet High School

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Applications in engineering

Vlad, Jean Monnet High School

The distance between two inaccessible points

Applications in engineering

Nicoli M.Gaudeamus High School, Moldova

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Applications in engineering

Daniel P.Gaudeamus High School, Moldova

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Applications in engineering

Zlata, Gaudeamus High School, Moldova

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Applications in engineering

Cristian, Gaudeamus High School, Moldova

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Applications in engineering

Mariela, Gaudeamus High School, Moldova

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Applications in engineering

Gaudeamus High School, Moldova

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Applications in engineering

Gaudeamus High School, Moldova

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Applications in engineering

Vlad V.Gaudeamus High School, Moldova

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Applications in engineering

Evghenii.Gaudeamus High School, Moldova

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Applications in engineering

Mihai N.Gaudeamus High School, Moldova

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Applications in engineering

ThaisLycée BrocéliandeFrance

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Applications in engineering

ClaireCité Scolaire Brocéliande France

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Applications in engineering

Miruna Iscu Jean Monnet High School

2 pulleys are nailed to 2 beams. The rope passing through the pulley supports a weight. The weights are 4.6 m from pulley A and 4 m from pulley B. If the pulleys are 6 m apart, find the angle between the ropes on the weights.

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Applications in Physics

EvenCité Scolaire BrocéliandeFrance

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Applications in Physics

Arina B.Gaudeamus High School, Moldova

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Applications in Physics

Daniel P.Gaudeamus High School, Moldova

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Applications in Physics

Angelina S.Gaudeamus High School, Moldova

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Applications in Physics

Briana T.Gaudeamus High School, Moldova

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Applications in Physics

MădălinaGaudeamus High School, Moldova

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Applications in Physics

Gaudeamus High School, Moldova

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Applications in Physics

MarielaGaudeamus High School, Moldova

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Applications in Physics

MădălinaGaudeamus High School, Moldova

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Applications in Physics

Gaudeamus High School, Moldova

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Applications in Physics

Arina B.Gaudeamus High School, Moldova

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Applications in medicine

Mariela D.Gaudeamus High School, Moldova

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Applications in medicine

Nicoli M.Gaudeamus High School, Moldova

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Applications in medicine

Sinus function curves used in paving stones

Daniel P.Gaudeamus High School, Moldova

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Applications in medicine

MădălinaGaudeamus High School, Moldova

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Applications in medicine

ZlataGaudeamus High School, Moldova

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Applications in medicine

Gaudeamus High School, Moldova

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Applications in medicine

Mădălina Gaudeamus High School, Moldova

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Applications in medicine

Gaudeamus High School, Moldova

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Applications in medicine

Eugeniu TGaudeamus High School, Moldova

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Applications in medicine

Vlad V.Gaudeamus High School, Moldova

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Applications in medicine

Călin.Gaudeamus High School, Moldova

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Applications in medicine

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Applications in medicine

Mihai N.Gaudeamus High School, Moldova

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Applications in medicine

Arina B.Gaudeamus High School, Moldova

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Applications in music

Nicoli M.Gaudeamus High School, Moldova

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Applications in music

Berra,Baruthane Secondary School,Turkey

Trigonometry is used in measuring the level or pitch of a sound wave or musical note. These notes are measured in hertz. People can use panels in rooms such as studios and turn them in different angles so that the music waves bounce off just right to make the song sound smooth and even.

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Applications in music

Çağan Aras, Baruthane Secondary School

Trigonometry plays an important role in music theory and construction. Sound waves move in a repeating wave pattern that can be represented graphically with the sine and cosine functions. A single note can be modeled on a sine curve and a chord can be modeled with multiple sine curves used in conjunction with each other.

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Applications in music

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Applications in music

Gaudeamus High School, Moldova

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Applications in music

Gaudeamus High School, Moldova

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Applications in music

MarielaGaudeamus High School, Moldova

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Applications in music

Mădălina G.Gaudeamus High School, Moldova

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Applications in music

EugeniuGaudeamus High School, Moldova

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Applications in music

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Applications in music

Sabina N.Gaudeamus High School, Moldova

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Applications in music

Dino Špondreht, Technical School Virovitica, CRO

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Applications in music

KeiaCité Scolaire Brocéliande France

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Applications in music

Arina B.Gaudeamus High School, Moldova

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Applications in the arts

Nicoli M.Gaudeamus High School, Moldova

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Applications in the arts

The regular polygon have 18 sides.

Andrei, Jean Monnet High School

Rosette with 18 petals

2 concentric circles in A have radii of 1 and 5, respectively. A third circle with diameter R–r rotates around point a from 20 to 20 degrees.1. Calculate the sum of the rosette petals obtained.2. Find the perimeter of the obtained polygon.

Applications in arts

https://i.pinimg.com/564x/31/02/22/31022292e8847339984641c54590542b.jpg

Daria, Jean Monnet High School, Romania

ACDEFGHI is a regular octogon with the side AC=2.Find the area of the circle sector AOC and the area of the octogon.

Art Design

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Applications in arts

ACDEFGHI - regular octogonAC=2

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Applications in the arts

Miruna, Jean Monnet High School, Romania

Flower - parametric curve

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Applications in the arts

Vlad, Jean Monnet High School, Romania

Flower - parametric curve

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Applications in arts

Miruna, Jean Monnet High School

Flower - parametric curve

Applications in the arts

Flower - parametric curve

Irina, Jean Monnet High School

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Applications in the arts

Parametric curve&Geometric transformations

-Dilatation, k=2 with centre the origin of system xOy-Central symmetry P(2.7; 0)-Axial symmetry - Oy

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Applications in the arts

SUDE BETÜL BARUTHANE SECONDARY SCHOOL TURKEY

Sinus function curves used in paving stones

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Applications in the arts

MarielaGaudeamus High School, Moldova

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Applications in the arts

MădălinaGaudeamus High School, Moldova

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Applications in the arts

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Applications in the arts

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Applications in the arts