Multiple choice

The angles of elevation of the top of a tower from two points on the ground at the distance 32 m and 18 m from its base and in the same straight line with it are complementary. The height (in m) of the tower is:

  1. 20

  2. 24

  3. 16

  4. 28
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B Correct answer
Explanation

Let angles be θ and 90°-θ. Then h/32=tan(θ) and h/18=tan(90°-θ)=cot(θ). Multiplying: (h/32)(h/18)=tan(θ)·cot(θ)=1, so h²=576 and h=24m. Complementary angles have tangents that are reciprocals.

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