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From a point on the ground, the angle of elevation to the top of a tower is 60 d

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Question: From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?

Options:

  1. 15 m
  2. 30 m
  3. 20 m
  4. 10 m

Correct Answer: 15 m

Solution: 

Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.

From a point on the ground, the angle of elevation to the top of a tower is 60 d

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
  1. 15 m
  2. 30 m
  3. 20 m
  4. 10 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
Correct Answer: 10√3 m
  • Step 1: Understand the problem. We have a tower that is 30 meters high and we want to find out how far away a point on the ground is from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
  • Step 4: Write the equation using the tangent function. We have tan(60°) = height/distance, which means tan(60°) = 30/distance.
  • Step 5: Know the value of tan(60°). The value of tan(60°) is √3.
  • Step 6: Substitute the value into the equation. Now we have √3 = 30/distance.
  • Step 7: Rearrange the equation to find distance. Multiply both sides by distance: distance * √3 = 30.
  • Step 8: Solve for distance. Divide both sides by √3: distance = 30/√3.
  • Step 9: Simplify if needed. This is the final answer for the distance from the point to the base of the tower.
  • Trigonometric Ratios – The question tests the understanding of the tangent function in right triangles, specifically how to relate the angle of elevation to the height and distance from the base.
  • Angle of Elevation – It assesses the ability to interpret the angle of elevation in a real-world context and apply it to find distances.
  • Right Triangle Properties – The problem involves recognizing the relationship between the sides of a right triangle formed by the tower, the ground, and the line of sight.
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