Trigonometry

(a)  angle(A)  =  38^o  and  angle(C)  =  85^o   --->   angle(B)  =  180^o - angle(A) - angle(B)  =  180^o - 38^o - 85^o  =  57^o

 

       Since you know side(c)  =  32 cm, you can use the Law of Sines to find sides a and b:

            side(a) / sin( angle(A) )  =   side(c) / sin( angle(C) )

            side(a) / sin( 38^o )  =  32 / sin( 85^o ) 

            side(a)  =  19.77 cm

 

            side(b) / sin( angle(B) )  =   side(c) / sin( angle(C) )

            side(b) / sin( 57^o )  =  32 / sin( 85^o ) 

            side(a)  =  26.94 cm

 

(b)  angle(A)  =  24^o  and  side(b)  =  12.5 m  side(c)  =  13.2 m

 

      This describes a S-A-S situation, so you can use the Law of Cosines:

            a²  =  b² + c² - 2·b·c·cos(A)

            a²  =  (12.5)² + (13.2)² - 2·(12.5)·(13.2)·cos(24)

            a  =  5.39 m

 

       You can use the Law of Sines to find angle(B)

            [Warning:  Don't use the Law of Sines to find the largest angle in a triangle unless you have to!]

        sin(B) / side(b)  =  sin(A) / side(a)

        sin(B) / 12.5  =  sin(24^o) / 5.39

        angle(B)  =  70.6^o

 

        By subtracting angle(C)  =  180^o - angle(A) - angle(B)  =  180^o - 24^o - 70.6^o   =  85.4^o