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A building has a height of 50 meters. If a ladder is placed against the building

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Question: A building has a height of 50 meters. If a ladder is placed against the building making a 60-degree angle with the ground, how long is the ladder?

Options:

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

Correct Answer: 25 meters

Solution: 

Using the sine function: sin(60) = height/ladder length. Therefore, ladder length = height/sin(60) = 50/sqrt(3)/2 = 50*2/sqrt(3) = 50*2/1.732 = 57.74 meters.

A building has a height of 50 meters. If a ladder is placed against the building

Practice Questions

Q1
A building has a height of 50 meters. If a ladder is placed against the building making a 60-degree angle with the ground, how long is the ladder?
  1. 25 meters
  2. 50 meters
  3. 100 meters
  4. 75 meters

Questions & Step-by-Step Solutions

A building has a height of 50 meters. If a ladder is placed against the building making a 60-degree angle with the ground, how long is the ladder?
  • Step 1: Understand the problem. We have a building that is 50 meters tall and a ladder that makes a 60-degree angle with the ground.
  • Step 2: Identify the relationship between the height of the building, the length of the ladder, and the angle. We can use the sine function from trigonometry.
  • Step 3: Recall the sine function definition: sin(angle) = opposite side (height) / hypotenuse (ladder length).
  • Step 4: For our problem, the opposite side is the height of the building (50 meters) and the angle is 60 degrees.
  • Step 5: Write the equation using the sine function: sin(60) = height / ladder length.
  • Step 6: Substitute the known values into the equation: sin(60) = 50 / ladder length.
  • Step 7: Solve for the ladder length: ladder length = height / sin(60).
  • Step 8: Calculate sin(60). It is equal to sqrt(3)/2.
  • Step 9: Substitute sin(60) into the equation: ladder length = 50 / (sqrt(3)/2).
  • Step 10: Simplify the equation: ladder length = 50 * (2/sqrt(3)).
  • Step 11: Calculate the final value: ladder length = 100/sqrt(3).
  • Step 12: To get a decimal value, calculate 100/sqrt(3) which is approximately 57.74 meters.
  • Trigonometry – The use of sine function to relate the height of the building to the length of the ladder at a given angle.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the ladder, the building, and the ground.
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