Questions: What is the length of the hypotenuse? If necessary, round to the nearest tenth. c= centimeters

Solution Steps

The Pythagorean 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. In this case, we have:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

We are given that one side has a length of 4.9 cm and the other side has a length of 2.6 cm. Substituting these values into the Pythagorean theorem, we get:

c² = 4.9² + 2.6²

Calculating the squares of the given lengths, we have:

c² = 24.01 + 6.76

Adding the squared values, we get:

c² = 30.77

To find the length of the hypotenuse (c), we need to find the square root of 30.77:

c = √30.77

Calculating the square root and rounding to the nearest tenth, we get:

c ≈ 5.5 cm

Final Answer: The final answer is $\boxed{5.5}$