Question

From the top of a 10 m tall tower the angle of depression of a point on a ground was
found to be 60°. How far is the point from the base of the tower.
​

Answer 1

Answer:

Distance = 5.78 m

Explanation:

tan 60° = p/b = √3 = 10/b

⇒b = 10/√3 = 10/1.73 = 1000/173 = 5.78 m

Answer 2

Given:

The height of the tower=10m

The angle of depression=60°

To find:

The distance of the point from the base of the tower

Solution:

The distance of the point from the base of the tower is 5.78m.

We can find the distance by following the given steps-

We know that the angle of depression from the top of the tower to a point on the ground is equal to the angle of elevation.

We will use the concept of trigonometry to determine the distance between the point on the ground and the tower's base.

So, let the angle of elevation be theta.

Theta=60°

Tan theta=Height of the tower/ Distance between point and base of the tower

On putting the values, we get

Tan 60°=10/Distance between point and base of the tower

$\sqrt{3}$=10/Distance between point and base of the tower

Distance between point and base of the tower=10/$\sqrt{3}$

We know that $\sqrt{3}$=1.732.

The distance between the point on the ground and the base of the tower=10/1.732

=5.78m

Therefore, the distance of the point from the base of the tower is 5.78m.