Question

A woman who is 5.75ft tall stands next to a lamp post that is 12ft tall. If its' shadow is 30ft long, how long is the shadow of the woman?

Answer 1

The length of shadow of the woman is 14.375 ft.

Explanation:

Here we are given that

Height of the woman = 5.75 ft

Height of the lamp post = 12 ft

Shadow of the lamp post = 30 ft

Let the angle of elevation of the light source be θ

By definition, in a right triangle, with respect to angle θ, we have;

tan(θ) = Opposite÷Adjacent

Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)

and tan(θ) = 12 ft ÷ 30 ft = 0.4

θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°

Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have

tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)

∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)

Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4

Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.