In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 2 feet and b = 8 feet, what is c? If necessary, round to the nearest tenth. c = __ feet

To find the length of the hypotenuse ( c ) in a right triangle where the lengths of the legs are ( a ) and ( b ), we can use the Pythagorean theorem, which states:

[

c = sqrt{a^2 + b^2}

]

Given ( a = 2 ) feet and ( b = 8 ) feet, we can substitute those values into the formula:

[

c = sqrt{(2)^2 + (8)^2}

]

[

c = sqrt{4 + 64}

]

[

c = sqrt{68}

]

[

c approx 8.2 text{ feet (rounded to the nearest tenth)}

]

So, the length of the hypotenuse ( c ) is approximately 8.2 feet.