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.

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.

To find the length of the hypotenuse ( c ) in a right triangle when you have the lengths of the legs ( a ) and ( b ), you can use the Pythagorean theorem, which states:

[

c^2 = a^2 + b^2

]

Given that ( a = 7 ) kilometers and ( b = 6 ) kilometers, you can plug in the values:

[

c^2 = 7^2 + 6^2

]

[

c^2 = 49 + 36

]

[

c^2 = 85

]

Now, take the square root to find ( c ):

[

c = sqrt{85} approx 9.2 text{ kilometers}

]

So, the length of the hypotenuse ( c ) is approximately 9.2 kilometers.