Multiple choice

The angles of depression of two houses from the top of a tower are 45° and 60°. One house is directly behind the other. What is the distance between the houses if the height of the tower is 120 m?

  1. 60 m

  2. 50.72 m

  3. 60.72 m

  4. 55 m
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B Correct answer
Explanation

Distance 1 = 120 / tan(45) = 120. Distance 2 = 120 / tan(60) = 120 / 1.732 = 69.28. Difference = 120 - 69.28 = 50.72 m.

AI explanation

The distance to the first house is found using the tangent of 45°, which gives 120 m. The distance to the second house is 120 divided by tan(60°), which equals 120 divided by √3, or approximately 69.28 m. The distance between the houses is the difference between these distances, 120 - 69.28 = 50.72 m.

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