My Learning Cart
?
Categories
Account

A tower is 40 meters high. From a point on the ground, the angle of elevation to

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

What’s inside this PDF?

Question: A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

Options:

  1. 20√3 meters
  2. 40 meters
  3. 20 meters
  4. 30 meters

Correct Answer: 20√3 meters

Solution: 

Distance = height / tan(angle) = 40 / tan(60°) = 40 / √3 = 20√3 meters.

A tower is 40 meters high. From a point on the ground, the angle of elevation to

Practice Questions

Q1
A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?
  1. 20√3 meters
  2. 40 meters
  3. 20 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A tower is 40 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?
  • Step 1: Understand the problem. We have a tower that is 40 meters high and we want to find out how far a point on the ground is from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 60 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 base).
  • Step 4: Write the formula. The formula we will use is: Distance = height / tan(angle).
  • Step 5: Plug in the values. The height of the tower is 40 meters and the angle is 60 degrees. So, we have: Distance = 40 / tan(60°).
  • Step 6: Calculate tan(60°). The value of tan(60°) is √3.
  • Step 7: Substitute tan(60°) into the formula. Now we have: Distance = 40 / √3.
  • Step 8: Simplify the expression. To make it easier, we can multiply the numerator and denominator by √3: Distance = (40√3) / 3.
  • Step 9: Final answer. The distance from the point to the base of the tower is approximately 20√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower and the distance from the base.
  • Angle of Elevation – Understanding how to apply the angle of elevation in right triangle problems.
  • Right Triangle Properties – Utilizing properties of right triangles to solve for unknown lengths.
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