Question

Alisha is a forester, she uses a clinometer to sight up the top of a tree. She measures an angle of 48°. She is standing 7.2m from the tree, and her eyes are 1.6m above the ground. How tall is the tree?​

Answer 1

9.6 m

Explanation:

The horizontal distance to the tree, the height of thr tree above 1.6 m, and the direct line of vision to the top of the tree form a right triangle.

The distance to the tree is the adjacent leg.

The height of the tree above 1.6 m is the opposite leg.

tan Θ = opp/adj

tan 48° = opp/7.2

opp = 7.2 m × tan 48°

opp = 8.0 m

Now we add the length of the opposite leg of the triangle to her height.

height = 8.0 m + 1.6 m

height = 9.6 m