What is the length of the hypotenuse in a right triangle with legs of length 6.5 inches and 5.5 inches?

To find the length of the hypotenuse ( c ) in a right triangle, we can use the Pythagorean theorem, which states:

[ c^2 = a^2 + b^2 ]

Given ( a = 6.5 ) inches and ( b = 5.5 ) inches, we can substitute these values into the equation:

1. Calculate ( a^2 ):

[ 6.5^2 = 42.25 ]

2. Calculate ( b^2 ):

[ 5.5^2 = 30.25 ]

3. Add these two results together:

[ c^2 = 42.25 + 30.25 = 72.50 ]

4. Now take the square root to find ( c ):

[ c = sqrt{72.50} approx 8.5 text{ inches} ]

So, c = 8.5 inches (rounded to the nearest tenth).