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A building is 80 meters tall. From a point on the ground, the angle of elevation

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Question: A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?

Options:

  1. 40√3 meters
  2. 80 meters
  3. 60 meters
  4. 100 meters

Correct Answer: 40√3 meters

Solution: 

Distance = height / tan(angle) = 80 / √3 = 80√3/3 meters.

A building is 80 meters tall. From a point on the ground, the angle of elevation

Practice Questions

Q1
A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?
  1. 40√3 meters
  2. 80 meters
  3. 60 meters
  4. 100 meters

Questions & Step-by-Step Solutions

A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?
Correct Answer: 80√3/3 meters
  • Step 1: Understand the problem. We have a building that is 80 meters tall and we want to find out how far away a point on the ground is from the base of the building.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the building is given as 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 building) divided by the adjacent side (distance from the base).
  • Step 4: Set up the equation. We can write the equation as tan(60 degrees) = height / distance.
  • Step 5: Substitute the known values. We know the height is 80 meters, so we have tan(60 degrees) = 80 / distance.
  • Step 6: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 7: Rewrite the equation. Now we have √3 = 80 / distance.
  • Step 8: Rearrange the equation to solve for distance. Multiply both sides by distance: distance * √3 = 80.
  • Step 9: Divide both sides by √3 to isolate distance. So, distance = 80 / √3.
  • Step 10: Simplify the answer. We can also express this as distance = 80√3 / 3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the point on the ground.
  • Angle of Elevation – Understanding the angle of elevation is crucial for setting up the right triangle in this scenario.
  • Right Triangle Properties – The relationship between the sides of a right triangle and the angles is fundamental to solving the problem.
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