In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7 kilometers and b = 6 kilometers, what is c? If necessary, round to the nearest tenth.
c = _____ kilometers
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7 kilometers and b = 6 kilometers, what is c? If necessary, round to the nearest tenth. c = _____ kilometers.
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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 ]
Here, ( a = 7 ) kilometers and ( b = 6 ) kilometers. Let’s calculate ( c ):
1. Square the lengths of the legs:
– ( a^2 = 7^2 = 49 )
– ( b^2 = 6^2 = 36 )
2. Add the squares of the legs:
– ( c^2 = 49 + 36 = 85 )
3. Take the square root to find ( c ):
– ( c = sqrt{85} )
4. Now, calculate ( sqrt{85} ) using a calculator:
– ( c approx 9.22 ) kilometers
5. Rounding to the nearest tenth, we get:
– ( c approx 9.2 ) kilometers
So, the length of the hypotenuse ( c ) is approximately 9.2 kilometers.