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?

The length of shadow of the woman is 14.375 ft.

Step-by-step 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.