SOLUTION: Find the longer of the two legs of a right triangle having a perimeter of 12 sqrt (3) if one acute angle is measured 30 degrees. Express your answer in the form: {{{ a+b* sqrt (3)

Question 424194: Find the longer of the two legs of a right triangle having a perimeter of 12 sqrt (3) if one acute angle is measured 30 degrees. Express your answer in the form:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the longer of the two legs of a right triangle having a perimeter of 12 sqrt (3) if one acute angle is measured 30 degrees. Express your answer in the form:
..
let x=hypotenuse
shorter leg =x/2 (side opposite the hypotenuse in a 30 deg right triangle=1/2 the hypotenuse.
longer leg =sqrt(3)x/2 (side adjacent is sqrt(3)/2 of the hypotenuse)
x+x/2+sqrt(3)x/2=12sqrt(3)
multiply by 2
2x+x+sqrt(3)x=24sqrt(3)
3x=23sqrt(3)
x=23sqrt(3)/3
longer leg=sqrt(3)x/2
=(sqrt(3)23sqrt(3)/3)/2
=(3*23/3)/2
=69/6=23/2 (ans) (note: there are no radicals in the answer)

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