A 24-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 6 feet from the base of the building. How high up the wall does the ladder reach? The ladder reaches ___ feet up the wall (round to the nearest hundredth)

23.24 feet

Step-by-step explanation:

Use the pythagorean theorem: a² + b² = c², where a and b are legs of the right triangle and c is the hypotenuse.

In this situation, the ladder is the hypotenuse of the triangle, and the distance from the base of the building is the long leg.

Plug in the ladder length as c and plug in the distance from the base of the building as a:

a² + b² = c²

(6²) + b² = (24)²

36 + b² = 576

b² = 540

b = 23.24

So, the ladder reaches approximately 23.24 feet up the wall

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step-by-step explanation: