Sylvia is replacing a piece of siding on her house. To make the 12 ft ladder stable
while she works, she places the ladder 5 ft away from the house. How high up on the house is the siding that she is replacing?
To solve this problem, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square 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 is the hypotenuse and the distance from the ladder to the house is one of the other sides. Let's call the height of the ladder h and the distance from the ladder to the house d.
According to the Pythagorean theorem, we have:
h^2 = 5^2 + d^2
We also know that the ladder is 12 ft long, so h = 12.
Substituting this information into the equation, we have:
12^2 = 5^2 + d^2
144 = 25 + d^2
Now, let's solve for d^2:
d^2 = 144 - 25
d^2 = 119
Taking the square root of both sides, we have:
d = √119
d ≈ 10.92
Therefore, the height of the siding that Sylvia is replacing is approximately 10.92 ft.