Pythagorean Theorem Word Problems
If you place a 28-foot ladder against the top of a 15-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, the height of the building is one side, and the distance from the bottom of the ladder to the bottom of the building is the other side.
Let's label the height of the building as "a", the distance from the bottom of the ladder to the bottom of the building as "b", and the length of the ladder as "c".
Using the Pythagorean Theorem, we have:
a^2 + b^2 = c^2
Plugging in the given values, we have:
15^2 + b^2 = 28^2
225 + b^2 = 784
b^2 = 784 - 225
b^2 = 559
Taking the square root of both sides, we get:
b = √559 ≈ 23.6
Therefore, the bottom of the ladder will be approximately 23.6 feet from the bottom of the building.