Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding

Answer 1

To find the height the ladder will reach, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's represent the height of the ladder as "h". The base of the ladder is 6 ft, and the length of the ladder (the hypotenuse) is 12 ft. Using the Pythagorean theorem, we can write the equation:

6^2 + h^2 = 12^2
36 + h^2 = 144
h^2 = 144 - 36
h^2 = 108

Taking the square root of both sides, we get:

h = √108 ≈ 10.4

Therefore, the ladder will reach a height of approximately 10.4 ft.