Real-life applications of Presented by: fleurenz villar

wHAT IS TRIGONOMETRY? TRIGONOMETRY is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. "SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent “SOH” stands for Sine = Opposite / Hypotenuse “CAH” stands for Cosine = Adjacent / Hypotenuse “TOA” stands for Tangent = Opposite / Adjacent

CAN TRIG FUNCTIONS BE APPLIED IN OUR EVERYDAY LIFE? YES!

pHYSICS: CRIMINOLOGY: NAVIGATION: TRIG is used to find components of vectors and model the mechanics of waves CRIMINOLOGY: TRIG IS USED TO CALCULATE A PROJECTILE’S TRAJECTORY IN ORDER TO ESTIMATE WHAT MIGHT HAVE CAUSED A COLLISION IN A CAR ACCIDENT OR HOW DID AN OBJECT FALL DOWN FROM SOMEWHERE OR IN WHICH ANGLE WAS A BULLET SHOT NAVIGATION: TRIG IS USED TO SET DIRECTIONS (N/E/W/S) ON THE COMPASS. IT IS ALSO USED TO FIND THE DISTANCE OF THE SHORE FROM A POINT IN THE SEA AND TO SEE THE HORIZON.

IT CAN BE APPLIED IN CONSTRUCTION MEASURING FIELDS, LOTS, AND AREAS MAKING WALLS PARALLEL AND PERPENDICULAR ROOF INCLINATION DETERMINING THE HEIGHT OF THE BUILDING, WIDTH, LENGTH ETC.

Finding the height of a building if you know the distance from where you observe the building and the angle of elevation you can easily find the height of the building. Similarly, if you have the value of one side and the angle of depression from the top of the building you can find another side in the triangle, all you need to know is one side and angle of the triangle.

EXAMPLE: JIMMY WANTS TO MEASURE THE HEIGHT OF A BUILDING. HE WALKS EXACTLY 100 FEET FROM THE BASE OF THE BUILDING AND LOOKS UP. THE ANGLE FROM THE GROUND TO THE TOP OF THE BUILDING IS 33 DEGREES. HOW TALL IS THE BUILDING TO THE NEAREST FOOT?

Therefore… TAN = OPPOSITE ADJACENT TAN 33 = X 100 100(TAN33)=X (But since we are asked to round to the nearest foot..) X = 65 OPPOSITE ADJACENT WE KNOW THAT: 100 is ADJACENT to the angle of elevation (33o) and X is OPPOSITE to the angle of elevation. (We learned that if we are given OPPOSITE and ADJACENT, we are going to use TAN). THE BUILDING IS 65 FT TALL. Therefore…

WHY DID I CHOOSE THIS APPLICATION OVER OTHERS? I CHOSE THIS SPECIFIC REAL-LIFE APPLICATION OF TRIG FUNCTIONS BECAUSE I THOUGHT IT WAS INTERESTING TO KNOW HOW TO FIND THE HEIGHT OF A BUILDING ESPECIALLY BECAUSE WE LIVE IN NEW YORK CITY WHERE WE’RE SURROUNDED WITH A LOT OF BUILDINGS WHEREVER WE GO.

REFERENCES: https://www.embibe.com/exams/real-life-applications-of-trigonometry/ http://www.tiem.utk.edu/~gross/bioed/bealsmodules/triangle.html