Howard is standing 87 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the water reservoir is about 60°. How far is Howard from the top of the water reservoir?

Question

Mathematics

Kamron Gilmore

11 December, 11:46

Howard is standing 87 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the water reservoir is about 60°. How far is Howard from the top of the water reservoir?

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Israel Hendrix · Answer 1

He is 174 yards from the top.

Since we have a 60° angle and a right angle, this is a 30-60-90 triangle. In these triangles, we can label the sides as t, t√3 and 2t, with t being the side opposite the 30° angle (the smallest side); t√3 being the side opposite the 60° angle (the middle side); and 2t being the hypotenuse (the longest side).

Our 87 yard side is across from the 30° angle, so it is t.

The side we are looking for is the hypotenuse, which would be 2t; 2 (87) = 174.