In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 3 millimeters and c = 9 millimeters, what is a? If necessary, round to the nearest tenth.
a = _____ millimeters
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 3 millimeters and c = 9 millimeters, what is a? If necessary, round to the nearest tenth. a = _____ millimeters
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To find the length of leg ( a ) in a right triangle, you can use the Pythagorean theorem, which states:
[ c^2 = a^2 + b^2 ]
Given:
– ( b = 3 ) millimeters
– ( c = 9 ) millimeters
First, we can square the values of ( b ) and ( c ):
[ c^2 = 9^2 = 81 ]
[ b^2 = 3^2 = 9 ]
Now, plug these values into the Pythagorean theorem:
[ 81 = a^2 + 9 ]
Next, subtract ( 9 ) from both sides:
[ 81 – 9 = a^2 ]
[ 72 = a^2 ]
Now, take the square root of both sides to find ( a ):
[ a = sqrt{72} ]
Calculating this gives:
[ a approx 8.485 ]
Rounding to the nearest tenth:
[ a approx 8.5 ]
So, the length of leg ( a ) is approximately 8.5 millimeters.