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A ladder 10 meters long leans against a wall, making an angle of 60 degrees with

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Question: A ladder 10 meters long leans against a wall, making an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

Options:

  1. 5 meters
  2. 10 meters
  3. 8.66 meters
  4. 7.5 meters

Correct Answer: 8.66 meters

Solution: 

Using sine, height = 10 * sin(60) = 10 * (√3/2) = 5√3 ≈ 8.66 meters.

A ladder 10 meters long leans against a wall, making an angle of 60 degrees with

Practice Questions

Q1
A ladder 10 meters long leans against a wall, making an angle of 60 degrees with the ground. How high does the ladder reach on the wall?
  1. 5 meters
  2. 10 meters
  3. 8.66 meters
  4. 7.5 meters

Questions & Step-by-Step Solutions

A ladder 10 meters long leans against a wall, making an angle of 60 degrees with the ground. How high does the ladder reach on the wall?
  • Step 1: Understand that the ladder forms a right triangle with the ground and the wall.
  • Step 2: Identify the length of the ladder, which is 10 meters.
  • Step 3: Recognize that the angle between the ladder and the ground is 60 degrees.
  • Step 4: Use the sine function to find the height the ladder reaches on the wall. The sine of an angle in a right triangle is the opposite side (height) divided by the hypotenuse (ladder length).
  • Step 5: Write the formula: height = ladder length * sin(angle).
  • Step 6: Substitute the values into the formula: height = 10 * sin(60).
  • Step 7: Calculate sin(60), which is √3/2.
  • Step 8: Multiply: height = 10 * (√3/2).
  • Step 9: Simplify the multiplication: height = 5√3.
  • Step 10: If needed, approximate the height: 5√3 is about 8.66 meters.
  • Trigonometry – The problem involves using the sine function to find the height reached by the ladder against the wall.
  • Right Triangle Properties – Understanding the relationship between the sides and angles of a right triangle formed by the ladder, the wall, and the ground.
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