My Learning Cart
?
Categories
Account

A tower is 100 meters high. From a point on the ground, the angle of elevation t

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

What’s inside this PDF?

Question: A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?

Options:

  1. 100√3 meters
  2. 50√3 meters
  3. 200 meters
  4. 150 meters

Correct Answer: 100√3 meters

Solution: 

Distance = height / tan(angle) = 100 / (1/√3) = 100√3 meters.

A tower is 100 meters high. From a point on the ground, the angle of elevation t

Practice Questions

Q1
A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
  1. 100√3 meters
  2. 50√3 meters
  3. 200 meters
  4. 150 meters

Questions & Step-by-Step Solutions

A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
  • Step 1: Understand the problem. We have a tower that is 100 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 to the top of the tower is given as 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 base).
  • Step 4: Write the formula. The formula we will use is: Distance = height / tan(angle).
  • Step 5: Substitute the values into the formula. Here, height = 100 meters and angle = 30 degrees. So, Distance = 100 / tan(30 degrees).
  • Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 7: Substitute tan(30 degrees) into the formula. Now we have Distance = 100 / (1/√3).
  • Step 8: Simplify the equation. Dividing by a fraction is the same as multiplying by its reciprocal, so Distance = 100 * √3.
  • Step 9: Final calculation. Therefore, the distance from the point to the base of the tower is 100√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the base using the angle of elevation.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tower, the distance from the base, and the angle of elevation.
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