Multiple choice

If the height of a pole and the distance between the pole and a man standing nearby are equal, what would be the angle of elevation to the top of the pole?

  1. 60°

  2. 90°

  3. 30°

  4. 45°
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D Correct answer
Explanation

Let height of pole be h and distance be d. Given h = d. The angle of elevation theta satisfies tan(theta) = h/d = 1. Therefore, theta = 45 degrees.

AI explanation

In the right triangle formed by the pole, the ground, and the line of sight, the tangent of the angle of elevation is the ratio of the height to the base. Given that the height and the distance are equal, the ratio is 1, which means tan(theta) = 1. The angle whose tangent is 1 is 45°. The result is 45°.

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