Multiple choice

The angle of elevation of the top of a vertical tower from two points A and B distance 100 m and 25 m from the base and in the same line with it are complementary. What is the height of the tower?

  1. 25

  2. 50

  3. 100

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the height be h and the angles be θ and (90°-θ). Then tan(θ) = h/100 and tan(90°-θ) = h/25. Since tan(90°-θ) = cot(θ) = 1/tan(θ), we get h/25 = 100/h, giving h² = 2500 and h = 50m.

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