Mr. Clark leaned a ladder against a wall. When placed, the ladder reaches the top of the wall. If the ladder is 35 feet long, and Mr. Allen places the ladder 28 feet from the wall, how tall is the wall? Use the picture below to help you. Show ALL of your work
Let's assume the height of the wall is "x" feet.
According to the given information, the ladder is 35 feet long and is leaned against the wall. We can represent the ladder's length as a hypotenuse of a right triangle, with the height of the wall as one side and the distance of the ladder from the wall as the other side.
By applying the Pythagorean theorem, we can write down the equation:
x^2 + 28^2 = 35^2
Simplifying the equation, we have:
x^2 + 784 = 1225
Subtracting 784 from both sides of the equation, we get:
x^2 = 1225 - 784
x^2 = 441
If we take the square root of both sides, we have:
x = √441
x = 21
Therefore, the height of the wall is 21 feet.