An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 66degrees ∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Question
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 66degrees ∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Solution
To solve this problem, we can use the trigonometric function cosine. The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, the adjacent side is the height of the electric box (22 feet) and the hypotenuse is the length of the ladder we're trying to find.
The formula is:
cos(θ) = adjacent/hypotenuse
We can rearrange this formula to solve for the hypotenuse (the length of the ladder):
hypotenuse = adjacent/cos(θ)
Substituting the given values:
hypotenuse = 22/cos(66)
Now, calculate the cosine of 66 degrees and divide 22 by that number. Remember to round your answer to the nearest tenth of a foot if necessary.
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