If a tree casts a shadow of 25ft at the same time that a 4ft person casts a shadow of 11 1/2 ft, find the height of the tree?

8.70 ft

Step-by-step explanation:

We are given;

Shadow of a tree as 25 ft Height of a person as 4ft Shadow of the person as 11.5 ft

We are required to determine the height of the tree

Step 1: Find the angle of elevation from the tip of the shadow to the top of the person.

tan θ = opp/adj

In this case; Opposite side = 4 ft

Adjacent side = 11.5 ft

Therefore; tan θ = (4 ft : 11.5 ft)

tan θ = 0.3478

θ = tan⁻¹ 0.3478

θ = 19.18°

Step 2: Calculate the height of the tree

The angle of elevation from the tip of the shadow of the tree to the top of the tree will 19.18°

Therefore;

Opposite = Height of the tree

Adjacent = 25 ft

Thus;

tan 19.18 ° = x/25 ft

x = tan 19.18° * 25 ft

= 0.3478 * 25 ft

= 8.695

= 8.70 ft

Therefore, the height of the tree is 8.70 ft