Question

The angle of depression of a boat B from the top K of a cliff HK, 300 metres high is 30°. Find the distance of the boat from the foot H of the cliff.

Answer 1

Let the required distance BH = x metres. HK is the cliff and ∠LKB is the angle of depression of B from K. 

Then, ∠KBH = ∠LKB = 30° ( ∵ LM || BH, alt. ∠s)

∴ In ΔBKH,

tan 30° = \(\frac{KH}{BH} = \frac{300}{x}\)

x = \(\frac{300}{tan\,30°}=\frac{300}{\frac{1}{\sqrt3}}\) = (300 x √3) meters 300√3 m.