Final answer:
Using the Pythagorean theorem, the length of the diagonal side of a triangular sail with sides 12 ft and 16 ft is calculated to be 20 ft.
Step-by-step explanation:
To find the length of the diagonal side of a triangular sail given two sides, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Assuming that the sail forms a right-angled triangle and the given sides are perpendicular to each other, we need to find the hypotenuse (diagonal side).
The formula derived from the Pythagorean theorem is c^2 = a^2 + b^2, where c is the hypotenuse, and a and b are the other two sides of the triangle.
Here, a = 12 ft, and b = 16 ft. Plugging these values into the formula gives us:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
Taking the square root of both sides, we find that c = 20 ft.
Therefore, the length of the diagonal side of the sail is 20 ft, which corresponds to answer choice (c).