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From a point 15 meters away from the base of a hill, the angle of elevation to t

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Question: From a point 15 meters away from the base of a hill, the angle of elevation to the top of the hill is 60°. What is the height of the hill?

Options:

  1. 10 meters
  2. 15 meters
  3. 20 meters
  4. 25 meters

Correct Answer: 20 meters

Solution: 

Using tan(60°) = height/15, height = 15 * √3 = 25.98 meters, approximately 26 meters.

From a point 15 meters away from the base of a hill, the angle of elevation to t

Practice Questions

Q1
From a point 15 meters away from the base of a hill, the angle of elevation to the top of the hill is 60°. What is the height of the hill?
  1. 10 meters
  2. 15 meters
  3. 20 meters
  4. 25 meters

Questions & Step-by-Step Solutions

From a point 15 meters away from the base of a hill, the angle of elevation to the top of the hill is 60°. What is the height of the hill?
  • Step 1: Understand the problem. You have a point 15 meters away from the base of a hill and you want to find the height of the hill.
  • Step 2: Draw a right triangle. The distance from the point to the base of the hill is one side (15 meters), the height of the hill is the other side, and the line from the point to the top of the hill is the hypotenuse.
  • Step 3: Identify the angle of elevation. The angle from the point to the top of the hill is 60°.
  • Step 4: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the hill) divided by the adjacent side (15 meters). So, tan(60°) = height / 15.
  • Step 5: Solve for height. Rearrange the equation to find height: height = 15 * tan(60°).
  • Step 6: Calculate tan(60°). The value of tan(60°) is √3 (approximately 1.732).
  • Step 7: Multiply to find the height. So, height = 15 * √3 = 15 * 1.732 = 25.98 meters.
  • Step 8: Round the answer. The height of the hill is approximately 26 meters.
  • Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
  • Angle of Elevation – The question involves calculating the height of an object using the angle of elevation from a specific distance.
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