Question

the shadow of a tower standing on a level ground is found to be 30m longer when the sun's altitude is 30 degrees then when it is 60 degree find the height of the tower

Answer 1

Answer: 15√3m

Step-by-step explanation:

See attachment!!!

Answer 2

Given:

Angles of elevation=60° and 30°

To find:

The height of the tower

Solution:

The height of the tower is 15$\sqrt{3}$m.

We can find the height by following the given steps-

Let us assume that the height of the tower be H and the length of the shadow from the foot of the tower to the point from where the angle of elevation is 60° is D.

We are given that the length of shadow increases by 30m when the angle of elevation decreases to 30°.

So, the length of the shadow from the foot of the tower to the point from where the angle of elevation is 30° is (D+30)m.

We will find the height by using the concept of trigonometry.

When the angle of elevation is 60°, the height/length of shadow=tan 60°.

H/D=$\sqrt{3}$

H=D$\sqrt{3}$

When the angle of elevation is 30°, the height/length of shadow=tan 30°.

H/(D+30)=1/  $\sqrt{3}$

H$\sqrt{3}$=D+30

On substituting the value of H,

D$\sqrt{3}$×$\sqrt{3}$=D+30

3D=D+30

3D-D=30

2D=30

D=15m

So, the value of H=D$\sqrt{3}$=15$\sqrt{3}$m.

Therefore, the height of the tower is 15$\sqrt{3}$m.