For a given right triangle, side a = 76.4 feet and side b = 39.3 feet. What is the length of side c to the nearest tenth of a foot?

To find the length of side c in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (side c) is equal to the sum of the squares of the other two sides (side a and side b).

The formula for the Pythagorean theorem is:

c^2 = a^2 + b^2

Given that side a = 76.4 feet and side b = 39.3 feet, we can substitute these values into the formula:

c^2 = (76.4)^2 + (39.3)^2

Now we'll calculate the value of c^2:

c^2 = 5853.76 + 1544.49

c^2 = 7398.25

To find the length of side c, we need to take the square root of both sides of the equation:

c = sqrt(7398.25)

Calculating the square root, we get:

c ≈ 86 feet (rounded to the nearest tenth of a foot)

Therefore, the length of side c is approximately 86 feet.