Question

A)
The acute angles in a right triangle are
and
. If
, what is
?
(1 point) θ ϕ sin ϕ = 0.25 cos θ
0.65
0.75
0.55
0.25
A)
A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of theirline of sight from the ground to the top of the tower is
? Round to the nearest hundredth.
(1 point) 65°
178.57 ft.
93.26 ft.
23.66 ft.
428.90 ft.

Answer 1

1) 0.25.
Reason: In a right triangle θ and ϕ are complementary, so cosθ = sinϕ. If sinϕ = 0.25, then cosθ = 0.25.

2) 93.26 ft.
Reason: tan(65°) = opposite/adjacent = 200/d, so d = 200 / tan(65°) ≈ 93.26 ft.