Question

An electrician leans an extension ladder against the outside wall of a house so that it

reaches an electric box 31 feet up. The ladder makes an angle of 78° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
a
necessary.

Answer 1

The length of the ladder can be found using the cosine function to relate the height it reaches on the wall to its length. By dividing the height of 31 feet by the cosine of 78° and rounding the result, the length of the ladder can be determined to the nearest tenth of a foot.

Step-by-step explanation:

To find the length of the ladder, we can use trigonometry since we know the angle the ladder makes with the ground and the height it reaches on the wall. Specifically, we'll use the cosine function, which relates the adjacent side (height the ladder reaches on the wall) to the hypotenuse (length of the ladder) in a right triangle.

Since we know the angle θ = 78° and the opposite side (height) is 31 feet, we can write the following equation:

cos(θ) = height/length of the ladder

To solve for the length of the ladder, rearrange the equation:

length of the ladder = height / cos(θ)

length of the ladder = 31 feet / cos(78°)

Using a calculator to find the cosine of 78 degrees and dividing 31 feet by that number will give us the length of the ladder. Don't forget to round your answer to the nearest tenth of a foot as required.