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From a point on the ground, the angle of elevation to the top of a tower is 30 d

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Question: From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 10 meters tall, how far is the point from the base of the tower?

Options:

  1. 5√3 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Correct Answer: 5√3 meters

Solution: 

Distance = height / tan(30) = 10 / (1/√3) = 10√3 meters.

From a point on the ground, the angle of elevation to the top of a tower is 30 d

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 10 meters tall, how far is the point from the base of the tower?
  1. 5√3 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 10 meters tall, how far is the point from the base of the tower?
  • Step 1: Understand the problem. We have a tower that is 10 meters tall and we want to find out how far away we are from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the tower is 30 degrees.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the base).
  • Step 4: Write the formula. We can express this as: tan(30 degrees) = height / distance.
  • Step 5: Plug in the values. We know the height is 10 meters, so we write: tan(30 degrees) = 10 / distance.
  • Step 6: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 7: Set up the equation. Now we have: 1/√3 = 10 / distance.
  • Step 8: Rearrange the equation to solve for distance. Multiply both sides by distance and then by √3: distance = 10 / (1/√3).
  • Step 9: Simplify the equation. This gives us distance = 10 * √3.
  • Step 10: Calculate the final answer. The distance from the point to the base of the tower is 10√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the base.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
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