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A person is 50 meters away from a tower. If the angle of elevation to the top of

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Question: A person is 50 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?

Options:

  1. 25√3 meters
  2. 50√3 meters
  3. 75√3 meters
  4. 100√3 meters

Correct Answer: 25√3 meters

Solution: 

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 25√3 meters.

A person is 50 meters away from a tower. If the angle of elevation to the top of

Practice Questions

Q1
A person is 50 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?
  1. 25√3 meters
  2. 50√3 meters
  3. 75√3 meters
  4. 100√3 meters

Questions & Step-by-Step Solutions

A person is 50 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?
  • Step 1: Understand the problem. You have a tower and a person standing 50 meters away from it. The angle of elevation to the top of the tower is 30 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the tower, the other side is the distance from the person to the tower (50 meters), and the angle between the ground and the line of sight to the top of the tower is 30 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 tower) divided by the adjacent side (distance from the person to the tower). So, tan(30 degrees) = height / 50 meters.
  • Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 5: Set up the equation. Now, you can write the equation: height = 50 * tan(30 degrees).
  • Step 6: Substitute the value of tan(30 degrees) into the equation. This gives you height = 50 * (1/√3).
  • Step 7: Simplify the equation. This means height = 50/√3.
  • Step 8: To make it easier to understand, you can multiply the numerator and denominator by √3. This gives you height = (50√3)/3.
  • Step 9: Calculate the height. The final height of the tower is approximately 25√3 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.
  • Angle of Elevation – Understanding the concept of angle of elevation is crucial for solving problems involving heights and distances.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is the opposite side and the distance from the tower is the adjacent side.
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