Multiple choice

The horizontal distance between 2 towers is 70 m.The angle of depression of the top of the first tower when seen from the top of the second tower is 30º. If the height of the second tower is 120 m, find the height of the first tower.

  1. 138.8 m

  2. 84.6 m

  3. 101.6 m

  4. 79.6 m

  5. None of these
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D Correct answer
Explanation

Let h be the height of the first tower. The difference in height is 120 - h. tan(30) = (120 - h) / 70. 1/sqrt(3) = (120 - h) / 70. 120 - h = 70 / 1.732 = 40.41. h = 120 - 40.41 = 79.59 m.

AI explanation

The difference in height between the two towers forms the opposite side of a right triangle, so tan 30 degrees equals the height difference divided by 70 meters. Since tan 30 degrees is 1 divided by root 3, the height difference is 70 divided by root 3, which rationalizes to approximately 40.41 meters. Subtracting this from the 120 meter height of the second tower gives the height of the first tower as 120 minus 40.41, which equals 79.59 meters, or approximately 79.6 meters.

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