In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 2 kilometers and b = 5 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 = 2 kilometers and b = 5 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:
[
c^2 = a^2 + b^2
]
Given:
– ( a = 2 ) kilometers
– ( b = 5 ) kilometers
Now plug in the values:
[
c^2 = (2)^2 + (5)^2
]
[
c^2 = 4 + 25
]
[
c^2 = 29
]
Now take the square root of both sides to find ( c ):
[
c = sqrt{29} approx 5.385
]
Rounding to the nearest tenth:
[
c approx 5.4 text{ kilometers}
]
So, the answer is:
c = 5.4 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 ]
Given:
– ( a = 2 ) kilometers
– ( b = 5 ) kilometers
Now, plug the values into the formula:
1. Square both a and b:
– ( a^2 = 2^2 = 4 )
– ( b^2 = 5^2 = 25 )
2. Add those squares together:
– ( c^2 = 4 + 25 = 29 )
3. Now take the square root to find c:
– ( c = sqrt{29} )
Using a calculator:
– ( c approx 5.385 )
Rounding to the nearest tenth gives:
– ( c approx 5.4 ) kilometers.
So, the final answer is:
c = 5.4 kilometers.