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

1 Answer
Oct 23, 2015

Answer:

#/_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#