Question

From the top of a 120 m high tower a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of repression as 60^o and 45° Find the distance between two cars.

Answer 1

Given:

Height of tower = 120 m

Let distance of car 1 (at 45°) from tower = x

Let distance of car 2 (at 60°) from tower = y

We know that,

\(\tan \theta = \frac {\text{Perpendicular}}{\text{Base}}\)

\(\tan 45° = \frac{120}x\)

⇒ \(1 = \frac{120}x\)

⇒ \(x = 120\)

\(\tan 60° = \frac{120}y\)

⇒ \(\sqrt 3 = \frac{120}y\)

⇒ \(y = \frac{120}{\sqrt 3}\)

⇒ \(y = \frac{120}{1.732}\)

⇒ \(y = 69.284\)

Now,

Distance = x + y

⇒ Distance = 120 + 69.284

⇒ Distance = 189.284

Hence, the distance between the 2 cars = 189.284 m.

Answer 2

Hence the between two men = 189.28 m