Question

The bottom of a ladder must be placed 2 feet from a wall. The ladder is 15 feet long. How far above the ground does the top of the ladder touch the

wall?
Round to the nearest tenth.
X=
feet

Answer 1

14.9

Explanation:

`{a}^(2) + {b}^(2) = {c}^(2) \\ {2}^(2) + {b}^(2) = {15}^(2) \\ 4 + {b}^(2) = 225 \\ 4 - 4 + {b}^(2) = 225 - 4 \\ {b}^(2) = 221 \\ \sqrt{ {b}^(2) } = √(221) \\ b = 14.866 \\ b = 14.9`

Answer 2

Answer: 14.9 feet

Explanation:

To find the distance above the ground that the top of the ladder touches the wall, we can use the Pythagorean Theorem.

We can set up the equation as follows:

a^2 + b^2 = c^2

Where c is the length of the ladder (15 feet), a is the distance above the ground that the top of the ladder touches the wall, and b is the distance that the bottom of the ladder is from the wall (2 feet).

Substituting these values and solving for a, we get:

a^2 + 2^2 = 15^2

a^2 + 4 = 225

a^2 = 221

a = sqrt(221)

Rounding to the nearest tenth, we get a = 14.866 feet. This is the distance above the ground that the top of the ladder touches the wall.

Therefore, X = 14.9 feet.