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An employee looks out his office window at a factory across the street. He estimates his office building and the factory building are 60 ft apart, the angle of depression to the base of the factory is 62°, and the angle of elevation to the top of the factory building is 23°.
-How tall is the factory across the street? Round to the nearest tenth of a foot.
A) approx. 122.5 ft
B) approx. 130.7 ft
C) approx. 138.3 ft
D) approx. 145.9 ft

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Quizplus · Accepted Answer

To find the height of the factory, we can use trigonometry, specifically the tangent function, which relates angles of a right triangle to the lengths of the sides opposite and adjacent to the angle. First, we find the height from the employee's eye level to the base of the factory using the angle of depression and the distance between the buildings. Then, we find the height from the employee's eye level to the top of the factory using the angle of elevation. The difference between these two heights gives the total height of the factory. The correct calculation leads to an answer of approximately 138.3 ft, making option C the correct choice.

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