My Learning Cart
?
Categories
Account

A person is 25 meters away from a tower and sees the top of the tower at an angl

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: A person is 25 meters away from a tower and sees the top of the tower at an angle of elevation of 30 degrees. What is the height of the tower?

Options:

  1. 12.5 meters
  2. 25 meters
  3. 25√3 meters
  4. 50 meters

Correct Answer: 12.5 meters

Solution: 

Using tan(30) = height/distance, height = distance * tan(30) = 25 * (1/√3) = 25/√3 meters.

A person is 25 meters away from a tower and sees the top of the tower at an angl

Practice Questions

Q1
A person is 25 meters away from a tower and sees the top of the tower at an angle of elevation of 30 degrees. What is the height of the tower?
  1. 12.5 meters
  2. 25 meters
  3. 25√3 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A person is 25 meters away from a tower and sees the top of the tower at an angle of elevation of 30 degrees. What is the height of the tower?
  • Step 1: Understand the problem. You have a tower and a person standing 25 meters away from it. The person sees the top of the tower at an angle of 30 degrees.
  • Step 2: Identify the right triangle formed by the tower, the ground, and the line of sight from the person to the top of the tower.
  • Step 3: In this triangle, the distance from the person to the tower is the base (25 meters), the height of the tower is the opposite side, and the angle of elevation is 30 degrees.
  • Step 4: Use the tangent function, which relates the angle to the opposite side (height) and the adjacent side (distance). The formula is: tan(angle) = opposite/adjacent.
  • Step 5: Substitute the known values into the formula: tan(30 degrees) = height / 25 meters.
  • Step 6: We know that tan(30 degrees) is equal to 1/√3. So, we can write: 1/√3 = height / 25.
  • Step 7: To find the height, multiply both sides by 25: height = 25 * (1/√3).
  • Step 8: Simplify the expression: height = 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 how to interpret the angle of elevation from a point to the top of an object.
  • 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.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks