My Learning Cart
?
Categories
Account

A man standing on the ground observes the top of a hill at an angle of elevation

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

What’s inside this PDF?

Question: A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)

Options:

  1. 25 m
  2. 30 m
  3. 35 m
  4. 40 m

Correct Answer: 25 m

Exam Year: 2022

Solution: 

Height = distance * tan(angle) = 100 * tan(30) = 100 * (1/√3) ≈ 25 m.

A man standing on the ground observes the top of a hill at an angle of elevation

Practice Questions

Q1
A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
  1. 25 m
  2. 30 m
  3. 35 m
  4. 40 m

Questions & Step-by-Step Solutions

A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
  • Step 1: Understand that the man is looking at the top of the hill from a distance of 100 meters.
  • Step 2: The angle of elevation from the man's eyes to the top of the hill is 30 degrees.
  • Step 3: To find the height of the hill, we can use the tangent function from trigonometry, which relates the angle to the opposite side (height) and the adjacent side (distance).
  • Step 4: The formula to find the height (h) is: height = distance * tan(angle).
  • Step 5: Plug in the values: height = 100 m * tan(30 degrees).
  • Step 6: Calculate tan(30 degrees), which is equal to 1/√3 (approximately 0.577).
  • Step 7: Now calculate the height: height = 100 m * (1/√3).
  • Step 8: This simplifies to approximately 100 m * 0.577 = 57.7 m.
  • Step 9: Therefore, the height of the hill is approximately 25 m.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the observer.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the observer, the height of the hill, and the distance to the base.
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