A ladder is placed against a wall such that it reaches the top of the wall. The foot of the ladder is 1.5 meters away from the wall and the ladder is inclined at an angle of 60⁰ with the ground. Find the height of the wall.

Consider AB as the wall and AC as the ladder whose foot C is 1.5 m away from B.

Take AB = x m and the angle of inclination is 60⁰.

From the figure, tanθ = $\frac{\mathrm{AB}}{\mathrm{CB}}$

Substituting the values, we get:

=> tan 60⁰ = $\frac{\mathrm{x}}{1.5}$

=> √3 = $\frac{\mathrm{x}}{1.5}$

=> x = √3 × 1.5 = 1.732 × 1.5

=> x = 2.5980 = 2.6 m

Hence, the height of the wall is 2.6 m.