Multiple choice

The horizontal distance between the two towers is 60 m. The angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, then the approximate height of the shorter tower is

  1. 115 m

  2. 100 m

  3. 80 m

  4. None of these
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A Correct answer
Explanation

Let h be the height of the shorter tower. The difference in height is 150 - h. tan(30) = (150 - h) / 60. 1/sqrt(3) = (150 - h) / 60. 60 / 1.732 = 150 - h. 34.64 = 150 - h. h = 115.36.

AI explanation

Let the height of the shorter tower be H, making the difference in height between the two towers 150 minus H. Using the angle of elevation formula from the shorter tower to the taller one gives tan(30 degrees) equals the difference in height divided by the horizontal distance of 60 meters. Substituting the values gives 1 divided by the square root of 3 equals 150 minus H divided by 60, and solving this results in H being approximately 115 meters.

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