Trigonometry in Real Life

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

Trigonometry in Real Life

eTwinning project

Trigonometry in Real Life

Applications in astronomy

Applications in architecture

Applications in navigation

Applications in Geography

Applications in engineering

Applications in Physics

Applications in medicine

Applications in music

Applications in arts

Applications in astronomy

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Arina B. Gaudeamus High School, Moldova

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Zlata D. Gaudeamus High School, Moldova

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Nicoli M. Gaudeamus High School, Moldova

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Daniel P. Gaudeamus High School, Moldova

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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.

Efsa baruthane Baruthane secondary school Turkey

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Mădălina B. Gaudeamus High School, Moldova

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Cristian-Patriciu, Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Mariela, Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Vlad T. Gaudeamus High School, Moldova

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Vlad V. Gaudeamus High School, Moldova

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Marius R. Gaudeamus High School, Moldova

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Evghenii, Gaudeamus High School, Moldova

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Mihai N. Gaudeamus High School, Moldova

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Louise, Cité Scolaire Brocéliande France

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Meiko Cité Scolaire Brocéliande France

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Léopold, Cité Scolaire Brocéliande France

Applications in architecture

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Cantacuzino Castle -Bușteni - Romania

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

The ceiling

Jean Monnet High School, Romania

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Modeling in GeoGebra, using the sine function

Ceiling detail

Jean Monnet High School, Romania

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Crooked Street

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

Applications in architecture

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Problem

Inspiration - mosaic Romanian Athenaeum-Bucharest

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.

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

Applications in architecture

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Solution

Applications in architecture

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Bodysgallen Hall, UK

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.

https://www.bodysgallen.com/

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.

Applications in architecture

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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.

Applications in architecture

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Maria A. Gaudeamus High School, Moldova

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Arina B. Gaudeamus High School, Moldova

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Zlata D. Gaudeamus High School, Moldova

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Mariela D. Gaudeamus High School, Moldova

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Macovei N. Gaudeamus High School, Moldova

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Daniel P. Gaudeamus High School, Moldova

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Angelina S. Gaudeamus High School, Moldova

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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.

Elif Ayse Baruthane secondary School Turkey

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

BEYZA,BARUTHANE SECONDARY SCHOOL,TURKEY

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Ogan, Baruthane Secondary School,Turkey

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Briana T.. Gaudeamus High School, Moldova

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Vlad, Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Mădălina G. Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Vlad V. Gaudeamus High School, Moldova

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Evghenii. Gaudeamus High School, Moldova

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Applications in architecture

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Broceliande team 1ere France

to be followed next page...

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Part 2

Broceliande team 1ere France

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Alwena Broceliande France

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Célestin Broceliande France

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Applications in navigation

Arina B. Gaudeamus High School, Moldova

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Applications in navigation

Arina B. Gaudeamus High School, Moldova

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Daniel P. Gaudeamus High School, Moldova

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Applications in navigation

Tunay Baruthane Secondary School

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.Gaudeamus High School, Moldova

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Zlata, Gaudeamus High School, Moldova

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Cristian-Patriciu. Gaudeamus High School, Moldova

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Mariela, Gaudeamus High School, Moldova

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Mădălina G Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Briana. Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Vlad T. Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Applications in navigation

Dragoș. Gaudeamus High School, Moldova

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Evghenii. Gaudeamus High School, Moldova

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Marius. Gaudeamus High School, Moldova

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Mihai N Gaudeamus High School, Moldova

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Applications in navigation

Sabina N. Gaudeamus High School, Moldova

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Jeanne Brocéliande high school France

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Applications in navigation

Applications in Geography

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A - Victory Square B - Charles de Gaulle Square C - Arch of Triumph AB=1.6 km AC=1.8 BC=0.7 Find A

Jean Monnet High School

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A - Victory Square B - Charles de Gaulle Square C - Arch of Triumph AB=1.6 km AC=1.8 BC=0.7 Find angle A.

Florentina, Jean Monnet High School

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Daniel P. Gaudeamus High School, Moldova

Applications in Geography

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Briana T. Gaudeamus High School, Moldova

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

BERA, BARUTHANE SECONDARY SCHOOL,TURKEY

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Mădălina B. Gaudeamus High School, Moldova

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Cristian, Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Mădălina G. Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Vlad T. Gaudeamus High School, Moldova

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Vlad V. Gaudeamus High School, Moldova

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Mariela. Gaudeamus High School, Moldova

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Dragoș. Gaudeamus High School, Moldova

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Marius Gaudeamus High School, Moldova

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Sabina N. Gaudeamus High School, Moldova

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Mihai N. Gaudeamus High School, Moldova

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Ambre Cité Scolaire Brocéliande France

Applications in engineering

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Instruments for measuring angles

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.

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

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

Denisa, Jean Monnet High School

Applications in engineering

Determining the height of a tower

Matei, Jean Monnet High School

Applications in engineering

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The height of a tree - experiment

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

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The height of a tree

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

Teofil, Jean Monnet High School

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The height of a tower

Irina, Jean Monnet High School

Applications in engineering

The distance between two inaccessible points

Vlad, Jean Monnet High School

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Nicoli M. Gaudeamus High School, Moldova

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Daniel P. Gaudeamus High School, Moldova

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Zlata, Gaudeamus High School, Moldova

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Cristian, Gaudeamus High School, Moldova

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Mariela, Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Vlad V. Gaudeamus High School, Moldova

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Evghenii. Gaudeamus High School, Moldova

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Mihai N. Gaudeamus High School, Moldova

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Thais Lycée Brocéliande France

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Claire Cité Scolaire Brocéliande France

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Applications in Physics

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.

Miruna Iscu Jean Monnet High School

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Applications in Physics

Even Cité Scolaire Brocéliande France

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Applications in Physics

Arina B. Gaudeamus High School, Moldova

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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

Mădălina Gaudeamus 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

Mădălina Gaudeamus High School, Moldova

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Applications in Physics

Gaudeamus High School, Moldova

Applications in medicine

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Arina B. Gaudeamus High School, Moldova

Applications in medicine

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Mariela D. Gaudeamus High School, Moldova

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Nicoli M. Gaudeamus High School, Moldova

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Sinus function curves used in paving stones

Daniel P. Gaudeamus High School, Moldova

Applications in medicine

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Mădălina Gaudeamus High School, Moldova

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Zlata Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Mădălina Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Eugeniu T Gaudeamus High School, Moldova

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Vlad V. Gaudeamus High School, Moldova

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Călin. Gaudeamus High School, Moldova

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Mihai N. Gaudeamus High School, Moldova

Applications in music

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Arina B. Gaudeamus High School, Moldova

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Nicoli M. Gaudeamus High School, Moldova

Applications in music

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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.

Berra,Baruthane Secondary School,Turkey

Applications in music

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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.

Çağan Aras, Baruthane Secondary School

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Gaudeamus High School, Moldova

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Gaudeamus High School, Moldova

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Mariela Gaudeamus High School, Moldova

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Mădălina G. Gaudeamus High School, Moldova

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Eugeniu Gaudeamus High School, Moldova

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Applications in music

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Sabina N. Gaudeamus High School, Moldova

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Dino Špondreht, Technical School Virovitica, CRO

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Keia Cité Scolaire Brocéliande France

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Applications in the arts

Arina B. Gaudeamus High School, Moldova

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Applications in the arts

Nicoli M. Gaudeamus High School, Moldova

Applications in arts

Rosette with 18 petals

The regular polygon have 18 sides.

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.

Andrei, Jean Monnet High School

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Applications in arts

Art Design

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

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

Daria, Jean Monnet High School, Romania

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Applications in the arts

ACDEFGHI - regular octogon AC=2

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Applications in the arts

Flower - parametric curve

Miruna, Jean Monnet High School, Romania

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Flower - parametric curve

Vlad, Jean Monnet High School, Romania

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Flower - parametric curve

Miruna, Jean Monnet High School

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Flower - parametric curve

Irina, Jean Monnet High School

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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

Sinus function curves used in paving stones

SUDE BETÜL BARUTHANE SECONDARY SCHOOL TURKEY

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Mariela Gaudeamus High School, Moldova

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Mădălina Gaudeamus High School, Moldova

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Applications in the arts