question_answer

A person observes the angle of elevation of a building as 30°. The person proceeds towards the building with a speed of \[25(\sqrt{3}-1)m/hour.\]After \[2\,hours\], he observes the angle of elevation as 45°. The height of the building (in meter) is  [UPSEAT 2003]

A) 100

B) 50

C) \[50(\sqrt{3}+1)\]

D) \[50(\sqrt{3}-1)\]

Correct Answer: B

Solution :

In \[\Delta PQR\], \[\tan {{30}^{o}}=\frac{PQ}{QR}\] Þ  \[\frac{1}{\sqrt{3}}=\frac{h}{50(\sqrt{3}-1)+h}\] Þ \[\sqrt{3}h=50(\sqrt{3}-1)+h\] Þ \[(\sqrt{3}-1)h\]            \[=50(\sqrt{3}-1)\] Þ \[h=50\,metre\].