If the rise is 5' and the base is 8', what is the hypotenuse?

To determine the hypotenuse in a right triangle where the rise is 5 feet and the base is 8 feet, the Pythagorean theorem is used. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Here, the rise (5 ft) can be represented as one side (a), and the base (8 ft) represents the other side (b). The formula can be expressed as:

c² = a² + b².

Substituting the known values:

c² = (5 ft)² + (8 ft)²,

c² = 25 ft² + 64 ft²,

c² = 89 ft².

Next, we take the square root of both sides to find the hypotenuse (c):

c = √89 ft²,

c ≈ 9.43 ft.

This value corresponds to the option indicating that the hypotenuse is approximately 9.43 feet, making it the correct choice. The calculation confirms the relationship between the triangle's sides and applies the Pythagorean theorem appropriately.