A ladder leaning against a vertical wall, makes an angle of 600 with the ground. The foot of the ladder is 3.5 m away from the wall. Find the length of the ladder.

A ladder leaning against a vertical wall, makes an angle of 60⁰ with the ground. The foot of the ladder is 3.5 m away from the wall. Find the length of the ladder.

Solution:

Let AC be the length of the ladder,

AB be the distance between the foot of the ladder and the base of the wall.

Thus, AB = 3.5 m  (Given)

In right angled triangle, ∆ ABC,

cos 60⁰ =  ^AB/_AC

∴¹/₂ = ^3.5/_AC

∴ AC = 3.5 × 2

∴ AC = 7 m.

∴  The length of the ladder is 7m.