8-3 Trigonometry

Trigonometry Trigonometry (Trig) is used to find missing angles and sides of a right triangle There are 3 common trig functions – Sine = sin θ – Cosine = cos θ – Tangent = tan θ θ = theta symbol for angle

Remember!!!!!!!! Hypotenuse – the longest side (across from the largest angle) Leg – the two sides of a right triangle forming the right angle –Adjacent Side – side next to the angle –Opposite Side – the side across from the angle θ Hypotenuse Adjacent to θ Opposite of θ

Trig Functions sinθ = opposite hypotenuse cosθ = adjacent hypotenuse tanθ = opposite adjacent θ

SOH CAH TOA s inθ = o pposite h ypotenuse c osθ = a djacent h ypotenuse t anθ = o pposite a djacent What does an Indian do when they stub their toe? They “soh cah toa”

Example 1 Find the value of x. 1)2) 70° x 8 60° x 10

Inverse of Trig Functions θ = sin -1 opp hyp θ = cos -1 adj hyp θ = tan -1 opp adj ( ) Calculator!!!! 2 nd sin 2 nd cos 2 nd tan

Example 2 Find the value of θ. 1) 2) θ 12 8 θ 6 18

Find the Missing Angle or Side

The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 feet. How far does the chair lift travel up the side of the mountain? d ° Example 3

A film crew in a helicopter records an overhead view of a skier’s downhill run from where she gets off the chair lift at the top to where she gets back on the chair lift for her next run. If the helicopter follows a level flight path, what is the length of that path. d ° Example 4

Angles of Elevation and Depression Angle of elevation – the angle between a horizontal line and the line of sight from an observer to an object at a higher level. Angle of depression – angle to an object at a lower angle.

Example 5 John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle of elevation to the top of the tree is 33º. How tall is the tree?

Example 6 A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41º. How far is the observer from the base of the building?

Example 7 An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?