In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 28 centimeters and b = 21 centimeters, what is c? If necessary, round to the nearest tenth.
c = ___ centimeters
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 28 centimeters and b = 21 centimeters, what is c? If necessary, round to the nearest tenth. c = ___ centimeters
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To find the length of the hypotenuse ( c ) in a right triangle, you can use the Pythagorean theorem, which states:
[
c^2 = a^2 + b^2
]
Given that ( a = 28 ) centimeters and ( b = 21 ) centimeters, we can substitute these values into the equation:
1. Calculate ( a^2 ) and ( b^2 ):
[
a^2 = 28^2 = 784
]
[
b^2 = 21^2 = 441
]
2. Add these values together:
[
c^2 = 784 + 441 = 1225
]
3. Take the square root to find ( c ):
[
c = sqrt{1225} approx 35.0 text{ centimeters}
]
So, the length of the hypotenuse ( c ) is approximately 35.0 centimeters.