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.
To solve this problem, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse of the right triangle, and the distance from the wall to where the ladder is placed is one of the other sides. Let's call the height of the wall 'h'.
Using the Pythagorean theorem, we can set up the following equation:
(h^2) + (28^2) = (35^2)
Simplifying the equation:
(h^2) + 784 = 1225
Subtracting 784 from both sides:
h^2 = 441
Taking the square root of both sides:
h = 21
Therefore, the wall is 21 feet tall.