SOLUTION: find the exact lengths of the legs of a 30-60-90 degree triangle if the hypotneuse is 12 cm

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Question 269934: find the exact lengths of the legs of a 30-60-90 degree triangle if the hypotneuse is 12 cm
Found 2 solutions by Alan3354, dabanfield:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Short side = 12*sin(30) = 6
Other side = 12*cos(30) = 12sqrt%283%29%2F2
= 6sqrt%283%29

Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact lengths of the legs of a 30-60-90 degree triangle if the hypotneuse is 12 cm
In a 30-60-90 right triangle the side opposite the 30 degree angle is half the hypotenuse, in this case 12/2 = 6cm. Let x be the remaining side.
Using the Pythagorean Theorem we have then:
12^2 = 6^2 + x^2
x^2 = 144 - 36
x^2 = 108
x = sqrt(108) = sqrt(36*3) = sqrt(36)*sqrt(3)
x = 6*sqrt(3)