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.

BC AC AB AC

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

ST SR 45 53 0.8491 RT SR 28 53 0.5283

sinB = sinC = sinθ = O H 21 29 20 ≈ 0.7241 ≈ 0.6897 cosB = cosC = 21 29 cosθ = A H 20 ≈ 0.7241 ≈ 0.6897

O H 94 x x sin62° 94 x 94 sin62° This step is not necessary 106.462

O H 100 ___ x sin44° 100 x 100 sin44° ______ This step is not necessary 143.956

72° 100ft x sinθ = O H __ sin72° = 100 ____ x × sin72° = 100 x = cosθ = A H __ cos62° = w 106.462 _______ 106.462 × cos62° = w 49.981ft ≈ w 72° 100ft x sinθ = O H __ sin72° = 100 ____ x × sin72° = 100 x = sin72° _______ x ≈ 105.146ft

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

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.

40° sinθ = O ___ H sin40° = x 20 20 × sin40° = x 12.856ft ≈ x cosθ = A ___ H cos40° = y 20 20 × cos40° = y 15.321 ≈ y 60° 1 √3 2 sinθ = O ___ H sin60° = sin60 ≈ 0.8660 cosθ = A cos60° = cos60° = 0.5000