When angle opposite to the unknown sides and other two sides are given then we use law of cosines
Law of cosine
[tex] c^2 = a^2 + b^2 - 2ab cos(c) [/tex]
From the given diagram
[tex] AB^2 = CB^2 + AC^2 - 2(CB)(AC) cos( c) [/tex]
CB = 108
AC= 55
Angle c= 59
[tex] AB^2 = 108^2 + 55^2 - 2(108)(55) cos( 59 ) [/tex]
[tex] AB^2 = 8570.34767 [/tex]
Take square root on both sides
AB = 92.6 m
To find out angle B we use sine law
[tex] \frac{sin(a)}{a} = \frac{sin b}{b} = \frac{sin c}{c} [/tex]
[tex] \frac{sin b}{b} = \frac{sin c}{c} [/tex]
From the figure
[tex] \frac{sin B}{AC} = \frac{sin C}{AB} [/tex]
[tex] \frac{sin B}{55} = \frac{sin 59}{92.6} [/tex]
sin(B) = 0.50916647
B = [tex] sin^{-1} [/tex](0.50916647)
Angle B= 30.61 degrees
