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An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 20 feet up. The ladder makes an angle of with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.

Ask by Guerrero Davey. in the United States
Jan 27,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The ladder is approximately 20.53 feet long.

Solution

To determine the length of the extension ladder, we can use trigonometric relationships in a right triangle.

Given:

  • Vertical height (opposite side): 20 feet
  • Angle with the ground:

Objective:

Find the length of the ladder (hypotenuse).

Approach:

  1. Identify the Right Triangle Components:
    • The ladder forms the hypotenuse.
    • The vertical height is the side opposite the angle.
  2. Use the Sine Function:
    Plugging in the known values:
  3. Solve for the Hypotenuse:
  4. Calculate :
  5. Compute the Length of the Ladder:

Conclusion:

The length of the ladder is approximately 20.53 feet.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Mind Expander

To find the length of the ladder, you can use the sine function from trigonometry. The height reached by the ladder (20 feet) represents the opposite side, while the length of the ladder represents the hypotenuse in a right triangle.
Using the sine formula:
Where is the length of the ladder. Rearranging gives:
Calculating (approximately 0.97437) gives us:
So, the length of the ladder is approximately 20.54 feet.
Did you know that ladders have been in use since ancient times? The oldest known ladder was discovered in a cave in the Middle East, dating back about 10,000 years! Ladders were even used by the Egyptians to build their great pyramids, showcasing how essential they are in construction and building projects throughout history.
In practice, always remember to position your ladder at the correct angle. A general rule is to place the base of the ladder one foot away from the wall for every four feet of height. This 4:1 ratio helps ensure the ladder is stable and prevents it from tipping over. So, if you’re climbing up to that electric box, safety should be your top priority!

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