In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 6.5 inches and b = 5.5 inches, what is c? If necessary, round to the nearest tenth.
c = _____ inches
What is the length of the hypotenuse in a right triangle with legs of length 6.5 inches and 5.5 inches?
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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).