SOLUTION: find the area of a 30-60-90 triangles with longest leg of 12

Question 570050: find the area of a 30-60-90 triangles with longest leg of 12

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the area of a 30-60-90 triangles with longest leg of 12
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The longest leg must be opposite the 60 degree angle.
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Let the shortest leg be "x".
Then the hypotenuse is "2x".
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Equation:
x^2 + 12^2 = (2x)^2
x^2 + 144 = 4x^2
3x^2 = 144
x^2 = 144/3
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x = 12sqrt(3)/3
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x = 4sqrt(3)
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Area = (1/2) leg*leg
Area = (1/2) 12*4sqrt(3)
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Area = 24sqrt(3) square units
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cheers,
Stan H.
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