In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7.7 centimeters and b = 2.8 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 = 7.7 centimeters and b = 2.8 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 when the lengths of the legs ( a ) and ( b ) are given, we can use the Pythagorean theorem:
[
c^2 = a^2 + b^2
]
Given:
– ( a = 7.7 ) cm
– ( b = 2.8 ) cm
First, we will calculate ( a^2 ) and ( b^2 ):
1. ( a^2 = 7.7^2 = 59.29 )
2. ( b^2 = 2.8^2 = 7.84 )
Next, we add these values:
[
c^2 = 59.29 + 7.84 = 67.13
]
Now, we take the square root of both sides to find ( c ):
[
c = sqrt{67.13} approx 8.2 , text{cm} quad (text{rounded to the nearest tenth})
]
Thus, the length of the hypotenuse ( c ) is approximately 8.2 centimeters.