A pole of 72 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.

Question: A pole of 72 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.

Solution:
sin30° = x/(72 - x)
⇒ 1/2 = x/(72 - x)
⇒ 72 - x = 2x
⇒ 3x = 72
⇒ x = 72/3 = 24

∴ The length of the broken part of the pole = 72 - 24 = 48 m