The Cosine Law states how one side of a triangle can be expressed using two other sides and angle between them.
Also recall the measurement of angles in degrees, minutes and seconds:
1^o1o is 1/360^(th)1360th part of a full circle;
1' = 1/60^(th) of 1^o
1" = 1/60^(th) of 1'
The Cosine Law:
![enter image source here]()
In our case we will use the following form:
b^2 = c^2+a^2-2cacosB
Using exact values,
b^2 = 9.5^2 + 6.2^2 - 2*9.5*6.2*cos(76^o20')
According to calculator,
cos(76^o20') = 0.23627288165
Therefore,
b^2 = 9.5^2 + 6.2^2 - 2*9.5*6.2*0.23627288165=
=100.85705454163
Hence, b~~10.0427613
Using the same Law of Cosines, we can find two other angles:
cos A = (-a^2+b^2+c^2)/(2bc)=
=(-6.2^2+10.0427613^2+9.5^2)/(2*10.0427613*9.5)~~0.800089526
Therefore, /_A=arccos(0.800089526)=0.643351883 (rad)
/_A=36.861347637786^o
cos C = (-c^2+a^2+b^2)/(2ab)=
=(-9.5^2+6.2^2+10.0427613^2)/(2*6.2*10.0427613)=0.39385658039
Therefore, /_C=arccos(0.39385658039)=1.16597277 (rad)
/_C=66.8053193213^o
