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From a point on the ground, the angle of elevation of the top of a hill is 30 de

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Question: From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

Options:

  1. 50 m
  2. 60 m
  3. 70 m
  4. 80 m

Correct Answer: 50 m

Solution: 

Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.

From a point on the ground, the angle of elevation of the top of a hill is 30 de

Practice Questions

Q1
From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
  1. 50 m
  2. 60 m
  3. 70 m
  4. 80 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
  • Step 1: Understand the problem. We have a point on the ground and a hill. We want to find the height of the hill.
  • Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the hill is 30 degrees.
  • Step 3: Know the distance from the point to the base of the hill. This distance is 100 meters.
  • Step 4: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the hill) divided by the adjacent side (distance to the base).
  • Step 5: Write the equation using the tangent of 30 degrees. We have tan(30°) = height / 100.
  • Step 6: Find the value of tan(30°). It is equal to 1/√3.
  • Step 7: Substitute the value of tan(30°) into the equation: 1/√3 = height / 100.
  • Step 8: Solve for height. Multiply both sides by 100: height = 100 / √3.
  • Step 9: Calculate the height. Using a calculator, 100 / √3 is approximately 57.74 meters.
  • Trigonometric Ratios – The question tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
  • Angle of Elevation – It assesses the ability to interpret the angle of elevation from a horizontal line to a point above it.
  • Right Triangle Properties – The problem involves applying properties of right triangles to find unknown side lengths using given angles.
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