Multiple choice

Points P and Q are on the opposite sides of a tower. The angle of elevation of the top of the tower from point P and Q are 60∘ and 30∘ respectively and the distance between P and Q is 64√3 m. What is the height of the tower (in m)?

  1. 48

  2. 54

  3. 35

  4. 64
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A Correct answer
Explanation

Let tower height = h. From point P: h/DP = tan60° = √3, so DP = h/√3. From point Q: h/DQ = tan30° = 1/√3, so DQ = h√3. Since P and Q are opposite sides: DP + DQ = h/√3 + h√3 = 64√3. Solving: h(1/√3 + √3) = 64√3. h(4/√3) = 64√3, so h = 48m. Options B (54m) and D (64m) don't satisfy the tangent relationships.

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