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 replace the siding?

Answer 1

Using the Pythagorean theorem, we can solve for the height of the ladder. Let the height be denoted as 'h'.

According to the problem, the base of the ladder is 6 ft from the base of the house, the ladder is 12 ft long, and the height of the ladder is 'h'.

Thus, we can form the equation:
6^2 + h^2 = 12^2

Simplifying this equation, we have:
36 + h^2 = 144

Subtracting 36 from both sides, we have:
h^2 = 108

Taking the square root of both sides, we have:
h ≈ √108 ≈ 10.4 ft

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