Multiple choice

The angles of elevation of the top of a tower from two points at the distances of $4\ m$ and $9\ m$ from the base of the tower and in the same straight line with it are complementary. The height of the tower is :

  1. $8\ m$
  2. $5\ m$
  3. $6\ m$
  4. $4\ m$
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C Correct answer
Explanation

Let height be h. Angles are theta and 90 - theta. Then tan(theta) = h/4 and tan(90 - theta) = cot(theta) = h/9. Multiplying these: tan(theta) * cot(theta) = (h/4) * (h/9) = 1. Thus h^2 = 36, so h = 6.

AI explanation

Let the height of the tower be h and the complementary angles of elevation be theta and 90 degrees minus theta. Using basic trigonometric ratios, we have tan theta equals h over 9 and tan(90 degrees minus theta), which is cot theta, equals h over 4. Multiplying these two equations gives tan theta multiplied by cot theta equals h squared over 36, so 1 equals h squared over 36. Solving for h yields a height of 6 m.

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