Using the Law of Cosine, we can find the side a.
cos(a)=cos(b)∗cos(c)+sin(b)∗sin(c)∗cos(A)
cos(a)=cos(100°)∗cos(78°)+sin(100°)∗sin(78°)∗cos(82°)
cos(a)=−0.74∗0.208+0.985∗0.978∗0.139=
=−0,154+0.134=0.02
a=arccos(0.02)=88.85° And then, using the Law of Sines, we can find B.
sin(a)/sin(A)=sin(b)/sin(B)
sin(B)=sin(b)∗sin(A)/sin(a)
sin(B)=sin(100°)∗sin(82°)/sin(88.85°)
sin(B)=0.9848∗0.9903/0.9998=0.9754
B=arcsin(0.9754)=77.27°Answer: 77.27°
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