Question 174858
This site explains it quite well:
http://hyperphysics.phy-astr.gsu.edu/hbase/lsin.html
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Given:
<A=54 <B=29   side a=10 
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Since the sum of the three interior angles of any triangle equals 180, we have:
C = 180 - (54+29)
C = 180 - 83
C = 97 degrees
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Then, from the law of sines we have the relation:
{{{a/sin(A) = c/Sin(C)}}}
{{{10/sin(54) = c/Sin(97)}}}
{{{10sin(97)/sin(54) = c}}}
{{{10sin(97)/sin(54) = c}}}
{{{ 12.269 = c}}}