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?(1 point)Responses13.4 ft.13.4 ft.10.4 ft.10.4 ft.108 ft.108 ft.180 ft.

Question

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?(1 point)Responses13.4 ft.13.4 ft.10.4 ft.10.4 ft.108 ft.108 ft.180 ft.

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Answer 1

Bot GPT 3.5 answered
8 months ago

To find the height that the ladder will reach, we can use the Pythagorean Theorem:

a^2 + b^2 = c^2

Where a is the distance from the bottom of the ladder to the base of the house (6 ft.), b is the height that the ladder will reach, and c is the length of the ladder (12 ft.).

So, we have:

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

Taking the square root of both sides, we have:

b ≈ √108
b ≈ 10.4 ft.

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