right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.

"sqrt" stands for "square root"

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Explanation:

Angle C is 60 degrees because adding the angles gets A+B+C = 180. Put another way, C = 180-A-B. Therefore, C = 180-30-90 = 60.

We have a 30-60-90 triangle with

Check out the diagram below.

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From here, we use the 30-60-90 triangle template. The short leg is x, the hypotenuse is 2x and the long leg is x*sqrt(3). The area of this template triangle is

area = 0.5*base*height

area = 0.5*(short leg)*(long leg)

area = 0.5*x*(x*sqrt(3))

area = 0.5*x^2*sqrt(3)

set this equal to 32*sqrt(3) and you should find that 0.5x^2*sqrt(3) = 32*sqrt(3) solves to x = 8

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Therefore we can say,

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.