A tower and a pole stand vertically. From a point between them on the ground, the angles of elevation of their tops are 45° and 30°, respectively. If the pole is 20 m high, and the point is equidistant from both, find the height of the tower.
Show answer & explanation
Correct answer: C
Explanation
Pole = 20 meters
Angle = 30° (Pole), 45° (Tower)
Distance from both = x
According to the formula:
tanθ = Height / Distance
For the Pole:
tan30° = 20 / x
1/√3 = 20 / x
x = 20√3
For the Tower:
tan45° = h / x
1 = h / (20√3)
h = 20√3 = 34.64 meters