Multiple choice

The angle of elevation of the top of the tower at the eye of an observer is found to be $45^{o}$. Find the height of the observer, if he is standing at a distance of $32.4\ m$ away from the tower and the height of the tower is $34\ m $.

  1. $1.6m$
  2. $2.4m$
  3. $2.8m$
  4. $3.8m$
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A Correct answer
Explanation

The observer is at distance 32.4m. The angle of elevation is 45 degrees, so the height of the tower above the observer's eye level is 32.4 * tan(45) = 32.4m. Total height = 34m. Observer height = 34 - 32.4 = 1.6m.

AI explanation

Let the observer's height be h and the horizontal distance to the tower be 32.4 meters. Since the angle of elevation to the top of the 34 meter tower is 45 degrees, the tangent ratio gives 1 equals (34 minus h) divided by 32.4. Solving this equation yields 34 minus h equals 32.4, so h equals 1.6 meters.

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