In a right triangle, a and b represent legs and c represents the hypotenuse. Determine the measure of side c if a = 28.2 cm and b = 12.8 cm. Express the answer to the nearest tenth centimeter.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Using this theorem, we have:
c^2 = a^2 + b^2
c^2 = (28.2 cm)^2 + (12.8 cm)^2
c^2 = 795.24 cm^2 + 163.84 cm^2
c^2 = 959.08 cm^2
Taking the square root of both sides, we get:
c = √959.08 cm
c ≈ 30.9 cm
Therefore, the length of side c is approximately 30.9 cm when rounded to the nearest tenth.