To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the base of the ladder to the house acts as one of the sides, and the height the ladder reaches acts as the other side.
Using the Pythagorean theorem, we can set up the equation:
(length of ladder)^2 = (distance from base to house)^2 + (height ladder reaches)^2
Substituting in the given values, we have:
(12 ft)^2 = (6 ft)^2 + (height ladder reaches)^2
Simplifying:
144 ft^2 = 36 ft^2 + (height ladder reaches)^2
108 ft^2 = (height ladder reaches)^2
Taking the square root of both sides:
height ladder reaches = sqrt(108) ft
Rounding to the nearest tenth, we find:
height ladder reaches ≈ 10.4 ft
Therefore, the ladder will reach approximately 10.4 ft high so that Sylvia can replace the siding.
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)
Responses
10.4 ft.
10.4 ft.
13.4 ft.
13.4 ft.
180 ft.
180 ft.
108 ft.
1 answer