A 30 -foot ladder is leaning against a building. The base of the ladder is 18 feet from the side of the building. How high does the ladder reach along the side of the building?

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Explanation:

Refer to the diagram below. We have a right triangle with known horizontal leg 18, and unknown vertical leg x. The hypotenuse is 30.

Let a = x, b = 18, c = 30.

Apply the Pythagorean theorem to solve for x

a^2 + b^2 = c^2

x^2 + 18^2 = 30^2

x^2 + 324 = 900

x^2 = 900-324

x^2 = 576

x = sqrt(576)

x = 24

The top of the ladder reaches 24 feet high.

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