NDA 2023 Maths · Mathematics · Heights and Distances · easy

From the top of a 50 m high cliff the angle of depression of a boat is 45^°. The distance of the boat from the foot of the cliff is

Single correct option

From the top of a

50

m high cliff the angle of depression of a boat is

45^\circ

. The distance of the boat from the foot of the cliff is

Show answer and solution

Answer: (D) $50$ m

The angle of depression equals the angle of elevation of the top from the boat, so

\tan45^\circ=\dfrac{50}{d}

and

d=50

m. The value

50\sqrt2

m is the line-of-sight distance (hypotenuse), not the horizontal distance asked.

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake