In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 68 kilometers and b = 51 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 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:

– ( a = 68 ) kilometers

– ( b = 51 ) kilometers

Step 1: Calculate ( a^2 ) and ( b^2 ).

[ a^2 = 68^2 = 4624 ]

[ b^2 = 51^2 = 2601 ]

Step 2: Add these two values together.

[ a^2 + b^2 = 4624 + 2601 = 7225 ]

Step 3: Take the square root of the sum to find c.

[ c = sqrt{7225} = 85 ]

So, the length of the hypotenuse (c) is:

c = 85 kilometers

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

[

c^2 = a^2 + b^2

]

Given that ( a = 68 ) kilometers and ( b = 51 ) kilometers, we can substitute these values into the formula:

[

c^2 = (68)^2 + (51)^2

]

Calculating the squares:

[

68^2 = 4624

]

[

51^2 = 2601

]

Now, add these two values:

[

c^2 = 4624 + 2601 = 7225

]

Next, take the square root of both sides to find ( c ):

[

c = sqrt{7225} = 85

]

Therefore, the length of the hypotenuse ( c ) is:

[

c = 85 text{ kilometers}

]

So, your answer is ( c = 85 ) kilometers.