Question

The length of shadow of a tower on the plane ground is `sqrt3` times the height of the tower.

The angle of elevation of sun is:

Options

• A. 45°

• B. 30°

• C. 60°

• D. 90°

Answer 1

Let AB be the tower and BC be the length of the shadow of the tower.

Here, θ is the angle of elevation of the sun.

Given, length of shadow of tower = `sqrt3` × Height of the tower

BC = `sqrt3` AB ... (1)

In right ΔABC

`tanO/=(AB)/(BC)`              `(tanO/=(\text{opposite side})/\text{opposite side})`

`thereforetanO/=(AB)/sqrt(AB)`                    `\text{Using} (1)`

`rArrtanO/=1/sqrt3`

`rArrtan=tan 30^@`                       `(thereforetan30^@=1/sqrt3)`

`rArrO/=30^@`

Thus, the angle of elevation of the sun is 30°.

Hence, the correct answer is B.