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A roofer props a ladder against a wall so that the base of the ladder is 4 feet away from the building. If the angle of elevation from the bottom of the ladder to the roof is 63°, how long is the ladder?

what is the answer? thank you​

A roofer props a ladder against a wall so that the base of the ladder is 4 feet away-example-1
User Chang
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We can use trigonometry to solve this problem. Let's call the length of the ladder "L". Then, we can use the tangent function to relate the angle of elevation to the length of the ladder:

tan(63°) = opposite/adjacent

In this case, the "opposite" side is the height of the building that the ladder reaches, and the "adjacent" side is the distance between the base of the ladder and the building. We know that the distance between the base of the ladder and the building is 4 feet, so we can plug in the values we have:

tan(63°) = height/4

Now we can solve for the height:

height = 4 * tan(63°)

Using a calculator, we get:

height ≈ 8.32 feet

Therefore, the length of the ladder is approximately:

L = √(4^2 + 8.32^2) ≈ 9.38 feet

So the length of the ladder is approximately 9.38 feet.
User Evkline
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