From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. What is the height of the cable tower?
Answer and explanation
Correct answer: A. 7(√3 + 1) m
- Step 1: Let distance between building and tower be d. In the lower triangle: tan(45°) = 7 / d => d = 7 m.
- Step 2: In the upper triangle, height above building is h: tan(60°) = h / d => √3 = h / 7 => h = 7√3 m.
- Step 3: Total height of tower = 7 + h = 7 + 7√3 = 7(√3 + 1) m.
Why not the others: 7(√3 - 1) m, 14√3 m and 7√3 m do not fit.
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