A triangle with angles of A=38, B=83 and C=59. Side opposite to angle C is measuring 20. How do you find lengths of other sides?

1 Answer
Alan P.
Aug 2, 2016

Use the Law of Sines to get
#a=14.365, b=23.151#

Explanation:

Given a triangle with angles #A, B, C# and corresponding opposite side lengths #a, b, c#
Law of Sines:
#color(white)("XXX")a/(sin(A))=b/(sin(B))=c/(sin(C))#

with the given data values
#color(white)("XXX")a/sin(38^@)=b/sin(83^@)=20/sin(59^@)#

#rArr#
#color(white)("XXX")a=sin(38^@)*20/sin(59^@) ~~14.36502#
and
#color(white)("XXX")b=sin(83^@)*20/sin(59^@)~~23.15075#

...The above is based on use of a calculator and the assumption that I didn't making typos in my data entry.

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