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^o# is #1/360^(th)# part of a full circle;
#1' = 1/60^(th)# of #1^o#
#1" = 1/60^(th)# of #1'#
The Cosine Law:
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#
