Question

Mr. Santos wanted to know the height of the tree. He observed from a point A that the angle of elevation of the top of the tree is 36 degrees. He then moved backwards 50 ft away from the initial point A, the angle of elevation of the top of the tree was 22 degrees. Find the height of the tree.

Answer 1

The height of the tree is approximately 45.51 ft.

Explanation:

The given information are;

The angle of elevation of the top of tree is 36 degrees

The distance backwards Mr. Santos moved = 50 ft.

The new angle of elevation of the top of the tree = 22 degrees

Therefore, we have;

The angle opposite to the 50 ft. side = 180 - (180 - 36) - 22° = 14°

Therefore, we have, by sine rule;

50/(sin(14)) = X/(sin(22))

X = (sin(22)) × 50/(sin(14)) ≈ 77.42 ft.

The height of the tree, T = X × sin(36°)

T = 77.42 ft. × sin(36°) ≈ 45.51 ft.

The height of the tree is approximately 45.51 ft