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

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.