How do you solve the triangle given #A=36^circ, a=8, b=5#?

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Answer 1 · 2017-01-08T20:41:14

Please open The Ambiguous Case and read it.

The reference says that if #a > b# then one possible triangle exists.

Use The Law of Sines to solve for #B#:

#sin(B)/b = sin(A)/a#

#sin(B) = sin(A)b/a#

#B = sin^-1(sin(A)b/a)#

#B = sin^-1(sin(36^@)5/8)#

#B ~~ 21.55^@#

We know A and B subtract them from 180:

#C ~~ 180 - 36 -21.55#

#C ~~ 122.45^@#

Use The Law of Sines to solve for c:

#c = sin(C)/sin(A)a#

#c = sin(122.45)/sin(36)8#

#c ~~ 11.49#