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serenity212 · May 15, 2008, 11:52 AM

Could you please help me with this trigonometric problem?
A triangle has two sides of length of 30cm and an angle of 50deg. Unfortunately, the position of the angle is not known. Sketch the 2 possible triangles and use them to work out the 2 possible lengths of the third side of the triangle.
Thanks.

galactus · May 16, 2008, 09:45 AM

One case is using the law of cosines. I include a diagram.

$a=\sqrt{b^{2}+c^{2}-2bccos({\theta})}$

$b=c=30, \;\ {\theta}=50$

$a=\sqrt{30^{2}+30^{2}-2(30)(30)cos(50)}$

The other case, use the law of sines.