Answer:
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
