Discussion
Two poles standing on the same side of a tower in a straight line with it, measure the angles of elevation of the top of the tower at 25º and 50º respectively. If the height of the tower is 70 m, find
Answer: B
Let AB be the tower and C and D the poles. AB = 70 m.
In Δ ABC, cot 50º = BC/AB
Or, cot (90º - 40º) = BC/70
Or, tan 40º = BC/70
Or, 0.8391 = BC/70
Or, BC = 0.8391 × 70 = 58.74 m.
In Δ ABD, cot 25º = BD/AB
Or, cot (90º - 65º) = BD/70
Or, tan 65º = BD/70
Or, 2.114451 = BD/70
Or, BD = 2.114451 × 70 = 148.01 m.
Hence, distance between people = CD = BD - BC
= 148.01 - 58.74 = 89.27 m.
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