Question

Picture is not drawn to scale.

Howard is standing 91 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the water reservoir is about 50°. About how far is Howard from the top of the water reservoir?
A.
58 yards
B.
119 yards
C.
142 yards
D.
76 yards

Answer 1

142 yards.

Explanation:

See the attached diagram.

Let the reservoir is AC and Howard is standing at B and AB = 91 yards.

Now, the angle of elevation from B to the top of the reservoir C is 50°.

Then using trigonometry,
`\cos 50 = (AB)/(BC) = (91)/(BC)`

⇒
`BC = (91)/(\cos 50)  = 141.57` ≈ 142 yards.

Therefore, the distance of Howard from the top of the reservoir is 142 yards. (Answer)