Question

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

Answer 1

the ratio of sides for the 30-60-90 triangle are
1 : √3 : 2

so let AB = √3 x
BC = x
AC = 2x

area = (1/2)(√3 x)(x) = 32^3 = 32768
x^2 = 65536/√3
x = 256/√(√3)

I will let you do the substitutions