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From a point on the ground, the angle of elevation to the top of a tower is 45 d

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Question: From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?

Options:

  1. 10 meters
  2. 15 meters
  3. 20 meters
  4. 25 meters

Correct Answer: 10 meters

Solution: 

Height = distance * tan(45) = 10 * 1 = 10 meters

From a point on the ground, the angle of elevation to the top of a tower is 45 d

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?
  1. 10 meters
  2. 15 meters
  3. 20 meters
  4. 25 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?
Correct Answer: 10 meters
  • Step 1: Understand the problem. We have a tower and a point on the ground that is 10 meters away from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the tower is 45 degrees.
  • Step 3: Recall the relationship in a right triangle. The height of the tower (opposite side) and the distance from the point to the base of the tower (adjacent side) form a right triangle.
  • Step 4: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For 45 degrees, tan(45) = 1.
  • Step 5: Set up the equation. Height of the tower = distance from the point to the base of the tower * tan(45 degrees).
  • Step 6: Substitute the values. Height = 10 meters * 1.
  • Step 7: Calculate the height. Height = 10 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the base.
  • Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line up to the line of sight to the top of the tower.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is the opposite side, the distance from the tower is the adjacent side, and the angle of elevation is given.
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