1. Sine and cosine are trig ratios for acute angles that involve the lengths of a leg and hypotenuse of a right triangle.
When looking UP at an object, the angle your line of sight makes with a horizontal line is called the angle of elevation.
When looking DOWN at an object, the angle your line of sight makes with a horizontal line is called the angle of depression.

2. BC AC AB AC

3. WV UW 16 34 8 17
0.4706 UV UW 30 34 15 17
0.8824

4. ST SR 45 53
0.8491 RT SR 28 53
0.5283

5. sinB =
sinC =
sinθ = O H 21 29 20 ≈ ≈
cosB =
cosC = 21 29
cosθ = A H 20 ≈ ≈

6. O H 94 x
x sin62° x 94
sin62°
This step is not necessary

7. O H
100
___ x
sin44° x
100
sin44°
______
This step is not necessary

8. 72° 100ft x sinθ = O H __ sin72° = 100 ____ x × sin72° = 100 x =
cosθ = A H __
cos62° = w
_______
× cos62° = w
49.981ft ≈ w
72°
100ft x
sinθ = O H __
sin72° =
100
____
x × sin72° = 100
x =
sin72°
_______
x ≈ ft

9. sinθ
sine
theta (θ)
sin35° x
___ 20
20 × sin35°
11.472ft
cosθ
cosine
theta (θ)
cos35° y 20
___
20 ×cos35°
16.383ft

10. SL = Short Leg
LL = Long Leg
Hyp = Hypotenuse
SL : LL : Hyp
x : x√3 : 2x 2 O H
___ 1 2
___
1/2 or 0.5 A H
___ √3
___ 2
Exact Ans.
(Preferred)
0.8660
Approx. Ans.

11. 40°
sinθ = O
___ H
sin40° = x 20
20 × sin40° = x
12.856ft ≈ x
cosθ = A
___ H
cos40° = y 20
20 × cos40° = y
≈ y
60° 1 √3 2
sinθ = O
___ H
sin60° =
sin60 ≈
cosθ = A
cos60° =
cos60° =