Final answer:
Using the Pythagorean theorem, we find that the height of Manuel's porch is 9 inches, as it is one side of a right triangle with the other sides being 40 inches (base) and 41 inches (hypotenuse).
Step-by-step explanation:
To determine the height of Manuel's porch, we can use the Pythagorean theorem since the ramp, the distance from the porch to the end of the ramp (the base), and the height of the porch form a right triangle. The Pythagorean theorem is expressed as a^2 + b^2 = c^2, where c represents the length of the hypotenuse (the ramp), and a and b represent the lengths of the other two sides. In this case, a is the height of the porch (which we are trying to find), and b is the base which is 40 inches. The ramp, c, is 41 inches long.
Following the theorem, we have:
a^2 + 40^2 = 41^2
If we solve for a,
a^2 = 41^2 - 40^2
a^2 = 1681 - 1600
a^2 = 81
Take the square root of both sides to find a:
a = √81
a = 9 inches
Therefore, the height of Manuel's porch is 9 inches.