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
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
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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.