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

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.