MHB Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=?

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Triangle ABC has an area of 25√3 and angle BAC measuring 30 degrees. The discussion focuses on finding the lengths of sides AC and BC, which are equal in this isosceles triangle. The area formula used is 1/2 * a^2 * sin(120°), leading to the equation 25√3 = 1/2 * a^2 * (√3/2). After solving, the correct side length is determined to be 10√3. The question about the answer being 10 * 4th root(3) is clarified as incorrect.
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Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=?

the answer I got was 10*4th root(3)

Is this correct?

I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never used it. I'm assuming it means side lengths of the triangle.
 
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Elissa89 said:
Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=?

the answer I got was 10*4th root(3)

Is this correct?

I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never used it. I'm assuming it means side lengths of the triangle.

the triangle is isosceles with $m\angle C = 120^\circ$ and $a = BC = b = AC$

$Area = \dfrac{1}{2}ab\sin(C)$

$25\sqrt{3} = \dfrac{1}{2}a^2 \sin(120^\circ)$

try again to solve for $a$
 
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