Question

From a point on a horizontal plane, the elevation of the top of the hill is 45°. The elevation becomes 75° after walking a distance of 500 m up a slope inclined at an angle of 15° to the horizon. The height of the hill is:

(a) 500√6 m

(b) 500√3 m

(c) 250√6 m

(d) 250√3 m

Answer 1

Correct option is (c) 250√6 m

From rt. \(\triangle\)PAQ,

\(\tan 45° = \frac{PQ}{AQ}\)

⇒ AQ = PQ = h

⇒ AP = h√2

∠BPM = 90° – 75° = 15° 

⇒ ∠APB = 45° – 15° = 30°

By sine rule on \(\triangle\)ABP, we have