A storm breaks a tree. The broken part of tree bends so that the top of the tree touches the ground and makes an angle of 60° with the horizontal plane. If the distance between the base of the tree and the point where top of tree touches the ground is 10 m, find the height of the tree?

July 28, 2023

Question	A storm breaks a tree. The broken part of tree bends so that the top of the tree touches the ground and makes an angle of 60° with the horizontal plane. If the distance between the base of the tree and the point where top of tree touches the ground is 10 m, find the height of the tree?
Type	multiple_choice
Option	37.3 m	correct
Option	17.3 m	incorrect
Option	27.3 m	incorrect
Option	20.3 m	incorrect

Solution

PQ = 10 and let RQ be X.

X = 10 √3

Now, PR² = X² + (10)²

PR2 = (10 √3)² + (10)²

= 300 + 100

PR2 = 400

PR = 20

Height of tree = RQ + PR

= X + 20

= 10 √3 + 20

= 10 * 1.73 + 20

= 17.3 + 20 = 37.3 meter (Option A)