A roofer's 30 FOOT ladder is against the side of a house. It is 8 YARDS from the ground to the top of the house. How far away from the house must he place the foot of the ladder in order to have the top of the ladder meet the roof of the house?
8 yards = 24 feet
24^2 + b^2 = 30^2
576 + b^2 = 900
b^2 = 324
b = 18 feet
To determine how far away from the house the foot of the ladder should be placed, we can use the concept of similar triangles and the Pythagorean theorem.
First, let's convert the measurements to the same unit. Since the ladder length is given in feet and the height of the house is given in yards, we need to convert the height to feet as well. There are 3 feet in a yard, so 8 yards is equal to 8 * 3 = 24 feet.
Let's assume that the distance from the foot of the ladder to the house is x feet. Now, we have a right triangle formed by the ladder, the distance x, and the height of the house.
Using the Pythagorean theorem, we can express the relationship between the ladder length, the distance, and the height:
(foot of the ladder to the house)^2 + (height of the house)^2 = (length of the ladder)^2
x^2 + 24^2 = 30^2
Simplifying this equation:
x^2 + 576 = 900
Subtracting 576 from both sides:
x^2 = 324
Taking the square root of both sides:
x = √324
x = 18
Therefore, the roofer must place the foot of the ladder 18 feet away from the house in order to have the top of the ladder meet the roof.