Answer: angle B = 15.04104216 degrees approximately
Round that however you need to.
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Explanation:
The lowercase letters a,b,c are used as side lengths while the uppercase letters A,B,C are the angles.
- Side 'a' is opposite angle A
- Side b is opposite angle B
- Side c is opposite angle c
From the diagram, we have the following info:
- side b = 22
- side c = 63
- side C = 48
Use the law of sines to find B
sin(B)/b = sin(C)/c
sin(B)/22 = sin(48)/63
sin(B) = 22*sin(48)/63
sin(B) = 0.25951089143656
B = arcsin(0.25951089143656)
B = 15.04104216 which is approximate
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Another possible value of B is
B = 180-arcsin(0.25951089143656) = 164.95896
Since
sin(15.04104216) = sin(164.95896) = 0.2595109
However, notice that this leads to
A+B+C = 180
A+ 164.95896 + 48 = 180
A + 212.95896 = 180
A = 180 - 212.95896
A = -32.95896
But we cannot have a negative angle. Therefore only one triangle is possible here.
The only solution is approximately B = 15.04104216
