A ladder is leaning against a wall. It makes a 60° angle with the wall. If the distance between the foot of the ladder and the wall is 7 meters, find the length of the ladder.

Question: A ladder is leaning against a wall. It makes a 60° angle with the wall. If the distance between the foot of the ladder and the wall is 7 meters, find the length of the ladder.

Solution:
Let BC be the wall and AC be the ladder.
Given, ∠BCA = 60° and AB = 7 meters.
∠B = 90°

In ΔABC,
sin 60° = AB/AC
⇒ √3/2 = 7/AC
⇒ √3 AC = 7 × 2
∴ AC = 14/√3

∴ The length of the ladder is 14/√3 meters.