SOLUTION: A 16-foot ladder is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is 5 ft from the building? Round to the nearest tenth.

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Question 84066This question is from textbook 0-618-20323-0
: A 16-foot ladder is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is 5 ft from the building? Round to the nearest tenth. This question is from textbook 0-618-20323-0

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Here, you can apply the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 to the right triangle formed by the ladder as the hypotenuse (side c), the wall of the building as the vertical side (side a) and the distance of the bottom of the ladder from the base of the building as the base of the right triangle, (side b).
So you are looking for the length of side a (the height the ladder reaches on the building) of the right triangle when you know the lengths of the other two sides.
c%5E2+=+a%5E2%2Bb%5E2 Substitute c = 16 ft. (The ladder) and b = 5 ft. (The distance of the bottom of the ladder from the base of the wall)
16%5E2+=+a%5E2%2B5%5E2 Simplify and solve for a.
256+=+a%5E2%2B25 Subtract 25 from both sides.
231+=+a%5E2 Take the square root of both sides.
a+=+15.19868 Round to the nearest tenth.
a+=+15.2 feet.