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
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
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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.