Question

a 10 foot ladder is leaning against a wall if the ladder reaches 8 feet up the wall how far is the base of the ladder from the wall.

Answer 1

Answer:

6ft

Step-by-step explanation:

This requires a little use of the Pythagorean Theorem.

The length of the leaning ladder is the hypothenuse of the right triangle formed by the wall and the ladder.

Hyp. = 10 ft Say this is C

The ladder height up the wall = 8 ft. Say this A.

We need to find the other leg, say B ,of the right triangle.

C^2 = A^2 + B^2

10^2 = 8^2 + B^2

100 = 64 + B^2 => B^2 = 100 - 64 = 36

B^2 = 36 so, B = 6 The positive square root since length is positive.

B = 6 ft This is how far the ladder bottom is from the wall.

Double Check: 10^2 = 8^2 + 6^2 or 100 = 64 + 36 Ok. As, it should. This check could be done mentally.

In addition, this is a Pythagorean Triple. (6, 8, 10).

Answer: 6 ft.

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