From the top of a cliff 92 m high, the angle of depression of a buoy is 20⁰. Calculate the nearest distance of the buoy from the foot of the cliff.

Consider AB as the cliff whose height is 92 m.

As C is a buoy making a depression angle of 20⁰.

We know that, ∠ACB = 20⁰

Take CB = x m

In a right-angle triangle ABC, cot20^o = $\frac{\mathrm{BC}}{\mathrm{AB}}$

=> cot20⁰ = $\frac{\mathrm{x}}{92}$

=> x = 92 × cot 20⁰

=> x = 92 × 2.7475

=> x = 252.7700 m

Hence, the distance of the buoy from the foot of the cliff is 252.77 m.