Check the picture below.
and since a triangle has a sum of 180° for all interior angles.
A = 180 - 39.34 - 25
A = 115.66
[tex]\bf \cfrac{sin(25^o)}{44}=\cfrac{sin(A)}{a}\implies \cfrac{sin(25^o)}{44}=\cfrac{sin(115.66^o)}{a} \\\\\\ a\cdot sin(25^o)=44\cdot sin(115.66^o)\implies a=\cfrac{44\cdot sin(115.66^o)}{sin(25^o)} \\\\\\ a\approx 93.8452\implies \stackrel{\textit{rounded up}}{a = 93.85}[/tex]
make sure your calculator is in Degree mode.
side note: there are two triangles possible which is why there are two answers per box
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Work Shown:
The lowercase letters are the sides, which are oppposite the uppercase letter angles. Eg: side b is opposite angle B
b = 66, c = 44, C = 25
Use the law of sines to determine angle B
sin(B)/b = sin(C)/c
sin(B)/66 = sin(25)/44
sin(B) = 66*sin(25)/44
sin(B) = 0.63392739261104
B = arcsin(0.63392739261104) or B = 180-arcsin(0.63392739261104)
B = 39.340476504461 or B = 180-39.340476504461
B = 39.340476504461 or B = 140.65952349554
B = 39.3 or B = 140.7
If angle B is 39.3, then angle A must be...
A+B+C = 180
A + 39.3 + 25 = 180
A + 64.3 = 180
A = 180 - 64.3
A = 115.7
Use this to find the length of side 'a'. Use the law of sines.
sin(A)/a = sin(C)/c
sin(115.7)/a = sin(25)/44
44*sin(115.7) = a*sin(25)
a*sin(25) = 44*sin(115.7)
a = 44*sin(115.7)/sin(25)
a = 93.8137144733656
a = 93.8
This triangle has the following sides and angles
sides: a = 93.8, b = 66, c = 44
angles: A = 115.7, B = 39.3, C = 25
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Repeat the same steps as above, but use B = 140.6595 instead
A+B+C = 180
A+140.6595+25 = 180
A+165.6595 = 180
A = 180-165.6595
A = 14.3405
A = 14.3
law of sines
sin(A)/a = sin(C)/c
sin(14.3405)/a = sin(25)/44
44*sin(14.3405) = a*sin(25)
a*sin(25) = 44*sin(14.3405)
a = 44*sin(14.3405)/sin(25)
a = 25.78708
a = 25.8
This triangle has the following sides and angles
sides: a = 25.8, b = 66, c = 44
angles: A = 14.3, B = 140.7, C = 25
