Multiple choice

From the top of a cliff, the angle of depression of car on the ground is $60^o$. If the car is at a distance of $30m$. from the cliff. Find the height of the cliff.

  1. $52$m
  2. $51$m
  3. $55$m
  4. $56$m
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A Correct answer
Explanation

The angle of depression from the cliff is equal to the angle of elevation from the car. Using trigonometry, tan(60) = height / 30. Since tan(60) = sqrt(3) is approximately 1.732, the height is 30 * 1.732 = 51.96m, which rounds to 52m.

AI explanation

Using the trigonometric ratio for tangent in a right triangle, tan(60 degrees) equals the height of the cliff divided by its horizontal distance from the car. We calculate sqrt(3) = height / 30. Multiplying 30 by sqrt(3) gives 51.96 meters, which rounds to 52 m.

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