Multiple choice

$ABC$ is a triangular park with $AB=AC=100$ cm. $A$ clock tower is situated at the midpoint of $BC$. The angles of elevation of the top of the tower from $A$ and $B$ are $cot ^{-1}3.2$ and $cosec ^{-1} 2.6$. The height of the tower is

  1. $25$ mt
  2. $50$ mt
  3. $100$ mt
  4. $50\sqrt{2}$ mt
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A Correct answer
Explanation

From cot(theta) = 3.2, the horizontal distance from A is 3.2h. From cosec(phi) = 2.6, sin(phi) = 5/13, so the horizontal distance from B is 2.4h. These form a 3-4-5 right triangle with AB = 100, giving h = 25 in the stated length units.

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