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 = sinθ– Cosine = cosθ– Tangent = tanθ

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

Hypo

tenu

se

Adjacent to θ

Opposite of θ

Trig Functions

sinθ = opposite hypotenuse

cosθ = adjacent hypotenuse

tanθ = opposite adjacent

θ

SOH CAH TOAsinθ = opposite

hypotenuse

cosθ = adjacent

hypotenuse

tanθ = opposite

adjacent

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°

x10

Inverse of Trig Functions

θ = sin-1 opp hyp

θ = cos-1 adj hyp

θ = tan-1 opp adj

( )( )

( )

Calculator!!!!2nd sin2nd cos2nd tan

Example 2

Find the value of θ.

1) 2)θ 12

8

θ6

18

Find the Missing Angle or Side

1016

x

x

16

12

17x

9.7x

24

32

1.

4.3.

2.

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?

d1200

20.75°

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

1200

20.75°

---------------------------------

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?