Two poles of equal height stand on either side of a road 80 m wide. From a point on the road between them, the angles of elevation of their tops are 60° and 30°. The height of each pole is:

Question

Accepted Answer

20√3 m. Let the point be x m from the nearer pole, so h = x·tan60° = √3x, and h = (80 − x)·tan30° = (80 − x)/√3. Equating: 3x = 80 − x, so x = 20 and h = 20√3 ≈ 34.64 m. (The point is not the midpoint — assuming x = 40 gives the wrong 40√3.)

Two poles of equal height stand on either side of a road 80 m wide. From a point on the road between them, the angles of elevation of their tops are 60° and 30°. The height of each pole is:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Trigonometry practice