Final answer:
Using the Pythagorean theorem, it was determined that the ladder, which forms a right triangle with the house and the ground, can only reach a maximum height of 20 feet. Therefore, it cannot reach a window that is 21.5 feet above the ground.
Step-by-step explanation:
To determine if the ladder will reach the window 21.5 feet above the ground, we will use the Pythagorean theorem because we have a right triangle formed by the side of the house, the ground, and the ladder. The formula for the Pythagorean theorem is:
a2 + b2 = c2
where c is the length of the hypotenuse (in this case, the ladder), and a and b are the lengths of the other two sides. In our question:
- a = 15 feet (distance from the base of the house to the bottom of the ladder)
- c = 25 feet (length of the ladder)
We need to find the length b, which would be the maximum height the ladder can reach against the house. Rearranging the formula gives us:
b2 = c2 - a2
b2 = 252 - 152
b2 = 625 - 225
b2 = 400
b = √400
b = 20 feet
So the maximum height the ladder can reach is 20 feet. Since the window is 21.5 feet above the ground, the ladder will not reach the window.