Howard is standing 89 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the water reservoir is about 55°. About how far is Howard from the top of the water reservoir?

Answer: Howard is 155.1 yards from the top of the water reservoir.

Step-by-step explanation:

A right angle triangle is formed. The distance between Howard and the bottom of the reservoir represents the adjacent side of the right angle triangle.

The distance of Howard from the top of the reservoir, h represents the hypotenuse of the triangle.

To determine h, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 55 = 89/h

h = 89/Cos 55 = 89/0.574

h = 155.1 yards