Multiple choice

The angle of elevation of the top of a tall building from the points M and N at the distances of 72m and 128m, respectively, from the base of the building and in the same straight line with it, are complementary. The height of the building (in m ) is:

  1. 96

  2. 90

  3. 80

  4. 84
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angles of elevation from M and N be α and (90°-α) since they are complementary. Then tan α = h/72 and tan(90°-α) = cot α = h/128. Using cot α = 1/tan α gives h/128 = 72/h, so h² = 72×128 = 9216, hence h = 96m. The answer matches option A.

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