Question

If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

To understand the fact of this question, consider the following example

I. A tower `2sqrt(3)` m high casts a shadow 2 m long on the ground, then the Sun’s elevation is 60°.

In ΔACB,

tan θ = `"AB"/"BC" = (2sqrt(3))/2` 

⇒ tan θ = `sqrt(3)` = tan 60°

∴ θ = 60°

II. A same height of tower casts a shadow 4m more from preceding point, then the Sun’s elevation is 30^°.

In ΔAPB,

tan θ = `"AB"/"PB" = "AB"/("PC" + "CB")`

⇒ tan θ = `(2sqrt(3))/(4 + 2) = (2sqrt(3))/6`

⇒ tan θ = `sqrt(3)/3 * sqrt(3)/sqrt(3) = 3/(3sqrt(3)`

⇒ tan θ = `1/sqrt(3)` = tan 30°

∴ θ = 30°

Hence, we conclude from above two examples that if the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is decreasing.