Question

A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance the two cars and how far is each car from the tower?

Answer 1

Let be the height of tower m and angle of depression from the top of tower are and respectively at two observing Car C and D.

Let m, m and,

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle,

Since

Again in a triangle

Hence the distance of first car from tower is m

And the distance of second car from tower is m

And the distance between cars is m.