Question

At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of the tree to the nearest foot.

Answer 1

14.43. That's your answer

Answer 2

Height of the tree = 14 feet

Explanation:

The following illustration will form a right angle triangle. The tree will form the height which is the opposite side. The shadow cast by the tree will form the adjacent side while the angle of elevation is 30° to the hypotenuse.

Using SOHCAHTOA principle

TOA will be used to solve this

since the adjacent side is given which is the length of the shadow and we are looking for the opposite side which is the height of the tree.

shadow length(adjacent) = 25 feet

height of tree(opposite) = y

angle made with the ground = 30°

tan 30° = opposite/adjacent

tan 30° = y/25

cross multiply

25 × tan 30 = y

y = 0.5773502692 × 25

y = 14.43375673 feet

Height of the tree = 14 feet