Multiple choice

The horizontal distance between two towers is 75 mand the angular depression of the top of the first toweras seen from the top of the second which is 160 m highis 45°. Find the height of the first tower

  1. 75M

  2. 85M

  3. 89M

  4. 65M

  5. 82M
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B Correct answer
Explanation

Let the towers be T1 and T2. T2 height = 160m. Horizontal distance = 75m. Angle of depression = 45 degrees. The difference in height between the two towers is 75 * tan(45) = 75m. Height of T1 = 160 - 75 = 85m.

AI explanation

The difference in height between the two towers is found using the tangent of the angle of depression, so tan 45 degrees equals the difference in height divided by 75 meters. Since tan 45 degrees is 1, the difference in height is 75 meters. Subtracting this from the 160 meter height of the second tower gives the height of the first tower as 85 meters.

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