The angles of elevation of the top of a tower from two points A and B at a distance of x m and (x + 5) m from the base of the tower of height 6 m and in the same straight line with it are complementary. What is the value of x?
A.4 m✓ Correct
B.5 m
C.6 m
D.9 m
Explanation
Let angles be α and 90° - α. tan α = 6/x and tan(90° - α) = cot α = 6/(x+5). Multiplying: tan α × cot α = 1 = 36/(x(x+5)). So x(x+5) = 36, x² + 5x - 36 = 0, (x+9)(x-4) = 0. So x = 4.
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