Question
Two persons, A and B, are looking at an object placed on
the top of a tower, from opposite sides of the pole. A is closer to the foot of the tower by 70 m than B. If the angles of elevation of the object by A and B are 60° and 45°, respectively, then the height (in m) of the tower (nearest to an integer) is: (√3 = 1.73)Solution
Given PQB = Tan 45° = (h/x) = h = x _________1 Therefore PQA = Tan 60° = (x/(x - 70)) √3 = (x/(x - 70)) = 1.73 = (x/(x - 70)) 1.73x – (70 x 1.73) = x 1.73x – 121.1 = x 1.73x – x = 121.1 0.73x = 121.1 X = (121.1/0.73) = 165.8
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