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
108 ft.
108 ft.
10.4 ft.
10.4 ft.
180 ft.
180 ft.
13.4 ft.
13.4 ft.
To find how high the ladder will reach when it is 6 feet away from the base of the house, we can use the Pythagorean Theorem since we have a right-angled triangle with the ladder as the hypotenuse and the distances from the house and the ground forming the other two sides.
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c² = a² + b²
In this case:
- c is the length of the ladder, which is 12 feet.
- a is the distance from the base of the house, which is 6 feet.
- We want to find the height the ladder reaches (b).
So, using the Pythagorean Theorem, we can solve for b:
12² = 6² + b²
144 = 36 + b²
144 - 36 = b²
108 = b²
b = sqrt(108)
Now let's calculate the square root of 108:
b ≈ 10.39 feet
Rounding to the nearest tenth, we get:
b ≈ 10.4 feet
Therefore, the ladder will reach approximately 10.4 feet high on the house. The correct answer is:
10.4 ft.