Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

A. $$\sqrt {mn\sqrt 3 } \,{\text{units}}$$

B. $$\sqrt {mn\root 4 \of 3 } \,{\text{units}}$$

C. $$\sqrt {3mn} \,{\text{units}}$$

D. $$\sqrt {mn} \,{\text{units}}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{Height}}\,{\text{of}}\,{\text{pole}} = PQ \cr & \tan {60^ \circ } = \sqrt 3 = \frac{{PQ}}{m} \cr & \tan {45^ \circ } = 1 = \frac{{PQ}}{n} \cr & {\text{Multiply}}\,{\text{both}}\,{\text{equations}} \cr & \sqrt 3 \times 1 = \frac{{PQ}}{m} \times \frac{{PQ}}{n} \cr & \therefore PQ = \sqrt {mn\sqrt 3 } \,{\text{units}} \cr} $$