In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7.3 millimeters and b = 5.9 millimeters, what is c? If necessary, round to the nearest tenth.
c = _____ millimeters
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7.3 millimeters and b = 5.9 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 using the Pythagorean theorem, we use the formula:
[
c = sqrt{a^2 + b^2}
]
Substituting the given values:
[
a = 7.3 text{ mm}
]
[
b = 5.9 text{ mm}
]
Calculating ( a^2 ) and ( b^2 ):
[
a^2 = 7.3^2 = 53.29
]
[
b^2 = 5.9^2 = 34.81
]
Now, adding these values:
[
a^2 + b^2 = 53.29 + 34.81 = 88.1
]
Now, take the square root to find ( c ):
[
c = sqrt{88.1} approx 9.4 text{ mm}
]
So, rounded to the nearest tenth, the length of the hypotenuse ( c ) is:
[
c approx 9.4 text{ millimeters}
]