How do you solve the triangle if C=60 degrees, A= 12, c=15?

1 Answer
Alan P.
Oct 23, 2015

/_A ~= 43.9^@
/_B ~= 76.1^@
b ~= 16.8

Explanation:

The Law of Sines tells us
color(white)("XXX")sin(A)/a=sin(B)/b=sin(C)/c

#sin(C)/c = sin(60^@)/15 = (sqrt(3)/2)/15 = sqrt(3)/30 ~= 0.057735

sin(A) = sin(C)/c*a = 0.057735*12 = 0.69282
/_A = arcsin(sin(A)) = arcsin(0.69282) ~= 43.85378^@

/_B = 180^@ - (/_A + /_C) = 180^@ - (43.85378^@+60^@) = 76.14622^@

sin(B)/b =sin(C)/c=0.057735
rarr b = sin(B)/0.057735 = sin(76.14622^@)/0.057735 = 16.81655

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