Question

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?

Answer 1

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.