Question

A pole `7 sqrt3` m high casts a shadow 21 m long on the ground, then the sun's elevation is ______.

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

A pole `7 sqrt3` m high casts a shadow 21 m long on the ground, then the sun's elevation is 30°.

Explanataion:

Let the height of the pole be BC, which casts a shadow AC on the ground.

Therefore, according to the question, AC = 21 m and BC = `7 sqrt3`.

Let Sun's angle of elevation is θ.

Then, according to diagram,

`tanθ = ("BC")/("AC")`

⇒ `tanθ = (7 sqrt3)/(21)`

= `1/(sqrt3)`

⇒ tanθ = tan30°   ...(Since tan30° = `1/(sqrt3)` )

⇒ θ = 30°

Therefore, the Sun's elevation is 30°