My Learning Cart
?
Categories
Account

From the top of a 50-meter high building, the angle of depression to a point on

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

What’s inside this PDF?

Question: From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

Options:

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

Correct Answer: 25√3 meters

Solution: 

Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

From the top of a 50-meter high building, the angle of depression to a point on

Practice Questions

Q1
From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
  1. 25√3 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Questions & Step-by-Step Solutions

From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
Correct Answer: 50√3 meters
  • Step 1: Understand the problem. We have a building that is 50 meters tall.
  • Step 2: The angle of depression from the top of the building to a point on the ground is 30 degrees.
  • Step 3: Visualize the situation. Draw a right triangle where the height of the building is one side (50 meters), the distance from the base of the building to the point on the ground is the other side, and the line of sight from the top of the building to the point on the ground is the hypotenuse.
  • Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the building) divided by the adjacent side (distance from the base).
  • Step 5: Write the formula: tan(angle) = opposite / adjacent. Here, tan(30 degrees) = height / distance.
  • Step 6: We know the height is 50 meters and tan(30 degrees) is 1/√3.
  • Step 7: Set up the equation: 1/√3 = 50 / distance.
  • Step 8: Rearrange the equation to find distance: distance = height / tan(30 degrees).
  • Step 9: Substitute the values: distance = 50 / (1/√3).
  • Step 10: Simplify the equation: distance = 50 * √3.
  • Step 11: Calculate the final answer: distance = 50√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the building to the angle of depression and the horizontal distance from the base.
  • Angle of Depression – Understanding that the angle of depression from the top of the building to the point on the ground is equal to the angle of elevation from that point to the top of the building.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is one leg, the distance from the base is the other leg, and the line of sight forms the hypotenuse.
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