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From a point on the ground, the angle of elevation to the top of a hill is 53.13

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Question: From a point on the ground, the angle of elevation to the top of a hill is 53.13 degrees. If the point is 40 meters away from the base of the hill, what is the height of the hill?

Options:

  1. 30 meters
  2. 40 meters
  3. 50 meters
  4. 20 meters

Correct Answer: 30 meters

Solution: 

Using the tangent function, tan(53.13) = height / 40. Therefore, height = 40 * tan(53.13) = 40 * 1.6 = 64 meters.

From a point on the ground, the angle of elevation to the top of a hill is 53.13

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a hill is 53.13 degrees. If the point is 40 meters away from the base of the hill, what is the height of the hill?
  1. 30 meters
  2. 40 meters
  3. 50 meters
  4. 20 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 53.13 degrees. If the point is 40 meters away from the base of the hill, what is the height of the hill?
  • Step 1: Understand the problem. We need to find the height of a hill given the angle of elevation and the distance from the point to the base of the hill.
  • Step 2: Identify the angle of elevation, which is 53.13 degrees.
  • Step 3: Identify the distance from the point to the base of the hill, which is 40 meters.
  • Step 4: Recall the tangent function in trigonometry, which relates the angle of elevation to the opposite side (height of the hill) and the adjacent side (distance from the point to the base).
  • Step 5: Write the formula using the tangent function: tan(angle) = opposite / adjacent.
  • Step 6: Substitute the known values into the formula: tan(53.13) = height / 40.
  • Step 7: Rearrange the formula to solve for height: height = 40 * tan(53.13).
  • Step 8: Calculate tan(53.13), which is approximately 1.6.
  • Step 9: Multiply 40 by 1.6 to find the height: height = 40 * 1.6 = 64 meters.
  • Trigonometric Functions – Understanding and applying the tangent function to relate angles and side lengths in right triangles.
  • Angle of Elevation – Recognizing the angle of elevation as the angle formed by the horizontal line and the line of sight to an object above the horizontal.
  • Right Triangle Properties – Using properties of right triangles to solve for unknown lengths using given angles and distances.
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