Answer:
To find the horizontal distance between the wall and the bottom of the ramp, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the plank forms the hypotenuse of the right triangle, and the height of the wall forms one of the other two sides. Let's label the horizontal distance we're trying to find as "x".
Using the Pythagorean theorem, we have:
x^2+19^2 = 31^2
Simplifying this equation, we get:
x^2 + 361961
Subtracting 361 from both sides, we get:
x^2 = 600
To solve for x, we take the square root of both sides:
x = √600 = 24.5 inches
