To determine how far away from the house the base of the ladder should be positioned, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
In this case:
- The height from the ground to the edge of the roof is the vertical side of the triangle (24 feet).
- The length of the ladder is the hypotenuse of the triangle (30 feet).
- The distance from the base of the ladder to the house is the horizontal side of the triangle (which we need to find).
The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the height (24 ft),
- \( b \) is the distance from the base of the ladder to the house,
- \( c \) is the length of the ladder (30 ft).
We can substitute the known values into the equation:
\[ 24^2 + b^2 = 30^2 \]
Calculating \( 24^2 \) and \( 30^2 \):
\[ 576 + b^2 = 900 \]
Now, subtract 576 from both sides:
\[ b^2 = 900 - 576 \] \[ b^2 = 324 \]
Now take the square root of both sides to solve for \( b \):
\[ b = \sqrt{324} = 18 \]
So the base of the ladder should be positioned 18 feet from the house.
Summary
- Height to roof edge: 24 feet
- Length of ladder: 30 feet
- Distance from base of ladder to house: 18 feet
Unfortunately, I'm unable to draw and attach a picture, but you can visualize this as a right triangle:
- The vertical leg (height) is 24 feet.
- The hypotenuse (ladder) is 30 feet.
- The horizontal leg (distance from the wall) is 18 feet.