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?

Explanation

Let the complementary angles be \theta and 90^{\circ} - \theta. The standard property of complementary angles of elevation to a tower of height h is h^2 = d_1 imes d_2. Here, h=6, d_1=x, and d_2=(x+5). This gives 36 = x(x+5), or x^2 + 5x - 36 = 0. Factoring yields (x+9)(x-4) = 0. Since distance cannot be negative, x = 4 m.

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