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

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Question: From a point on the ground, the angle of elevation to the top of a tower is 45°. If the point is 50 meters away from the base of the tower, what is the height of the tower?

Options:

  1. 25 meters
  2. 50 meters
  3. 70 meters
  4. 100 meters

Correct Answer: 50 meters

Solution: 

Using tan(45°) = height/50, height = 50 * 1 = 50 meters.

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

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tower is 45°. If the point is 50 meters away from the base of the tower, what is the height of the tower?
  1. 25 meters
  2. 50 meters
  3. 70 meters
  4. 100 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a tower is 45°. If the point is 50 meters away from the base of the tower, what is the height of the tower?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your eye level to the top of the tower.
  • Step 2: Recognize that when the angle of elevation is 45°, the height of the tower is equal to the distance from the point on the ground to the base of the tower.
  • Step 3: Identify that the distance from the point on the ground to the base of the tower is 50 meters.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height and distance: tan(angle) = height / distance.
  • Step 5: Substitute the values into the equation: tan(45°) = height / 50.
  • Step 6: Know that tan(45°) equals 1, so the equation becomes 1 = height / 50.
  • Step 7: Solve for height by multiplying both sides by 50: height = 50 * 1.
  • Step 8: Conclude that the height of the tower is 50 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 tower.
  • Right Triangle Properties – Understanding the properties of right triangles, specifically how to apply the tangent ratio in a right triangle formed by the height of the tower and the distance from the base.
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