Final answer:
To determine if a ramp length represents the hypotenuse of a right-angled triangle, we can use the Pythagorean theorem and check if the squares of the other two sides add up to the square of the hypotenuse.
Step-by-step explanation:
The length of the ramp, 15 ft, represents the potential hypotenuse of a right-angled triangle. To determine if it is a right-angled triangle, we can use the Pythagorean theorem. According to this theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume that the other two sides of the triangle are the base and the height. We can use the formula a² + b² = c², where a and b are the lengths of the base and height, respectively, and c is the length of the hypotenuse.
In this case, if we assume that the ramp length (15 ft) is the hypotenuse, we can square the lengths of the other two sides and check if they add up to the square of the hypotenuse. Let's say the base is x and the height is y:
x² + y² = 15²
Now, we can rearrange this equation to solve for the hypotenuse:
15² = x² + y²
225 = x² + y²
Now, let's check if there are any values of x and y that satisfy this equation. If there are, then the ramp length represents the hypotenuse of a right-angled triangle.
Note: While the length of the ramp alone does not guarantee that it represents the hypotenuse of a right-angled triangle, it is a possible representation.