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A tower is 60 meters high. From a point on the ground, the angle of elevation to

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Question: A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

Options:

  1. 30 meters
  2. 60 meters
  3. 45 meters
  4. 75 meters

Correct Answer: 60 meters

Solution: 

Distance = height / tan(angle) = 60 / 1 = 60 meters.

A tower is 60 meters high. From a point on the ground, the angle of elevation to

Practice Questions

Q1
A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?
  1. 30 meters
  2. 60 meters
  3. 45 meters
  4. 75 meters

Questions & Step-by-Step Solutions

A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?
  • Step 1: Understand that the tower is 60 meters high.
  • Step 2: Know that the angle of elevation to the top of the tower is 45 degrees.
  • Step 3: Recall that 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 for distance: Distance = height / tan(angle).
  • Step 5: Substitute the height (60 meters) and the angle (45 degrees) into the formula. Since tan(45 degrees) = 1, the formula becomes Distance = 60 / 1.
  • Step 6: Calculate the distance, which equals 60 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower and the distance from the base.
  • Angle of Elevation – Understanding the angle of elevation is crucial for determining the relationship between the height and distance.
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