In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 5 millimeters and b = 3 millimeters, what is c? If necessary, round to the nearest tenth.
c = _____ millimeters
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 5 millimeters and b = 3 millimeters, what is c? If necessary, round to the nearest tenth. c = _____ millimeters
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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
]
Given that ( a = 5 ) millimeters and ( b = 3 ) millimeters, we can substitute these values into the equation:
[
c^2 = 5^2 + 3^2
]
Calculating the squares:
[
c^2 = 25 + 9
]
[
c^2 = 34
]
Now, we take the square root of both sides to find ( c ):
[
c = sqrt{34} approx 5.831
]
Rounding to the nearest tenth, we have:
[
c approx 5.8 text{ millimeters}
]
So, ( c = 5.8 ) millimeters.