The angle of elevation of the top of a tower is 30° from a point on the ground. On moving 100 m closer to the base, the angle becomes 60°. Find the height of the tower.
Show answer & explanation
Correct answer: C
Explanation
Height of the tower = h meters
Distance from the initial point to the base of the tower = x meters.
New distance after moving 100 meters towards the base = (x − 100) meters
In the first case -
tan 30° = h/x
⇒ 1/√3 = h/x
⇒ x = √3h
In the second case -
tan 60° = h/(x − 100)
⇒ √3 = h/(x − 100)
⇒ x − 100 = h/√3
√3h − 100 = h/√3
3h − 100√3 = h
2h = 100√3
h = 50√3 meters