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A tower is standing on a horizontal ground. The angle of elevation of the top of

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Question: A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?

Options:

  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Correct Answer: 20 m

Solution: 

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

A tower is standing on a horizontal ground. The angle of elevation of the top of

Practice Questions

Q1
A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?
  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Questions & Step-by-Step Solutions

A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?
Correct Answer: 30 m
  • Step 1: Understand the problem. We have a tower and we want to find out how far a point on the ground is from the base of the tower.
  • Step 2: Identify the height of the tower. The height is given as 10√3 meters.
  • Step 3: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 30 degrees.
  • Step 4: Recall the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the tower).
  • Step 5: Write the formula for tangent. For our case, tan(30°) = height / distance.
  • Step 6: Substitute the known values into the formula. We know tan(30°) = 1/√3 and height = 10√3, so we have 1/√3 = 10√3 / distance.
  • Step 7: Rearrange the equation to solve for distance. Multiply both sides by distance to get distance * (1/√3) = 10√3.
  • Step 8: Multiply both sides by √3 to isolate distance. This gives us distance = 10√3 * √3.
  • Step 9: Simplify the right side. Since √3 * √3 = 3, we have distance = 10 * 3 = 30 meters.
  • Step 10: Conclude that the distance from the point to the base of the tower is 30 meters.
  • Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to relate the height of an object to the distance from it using angles of elevation.
  • Angle of Elevation – It assesses the ability to interpret the angle of elevation and apply it to find distances in a real-world context.
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