find the adjacent angle b of a right triangle with side c460

find the adjacent angle (b) of a right triangle with side c=460 and angles c=90 b=54 a=36

Solution

c=460 and angles C=90^o, B=54^o ,A=36^o

angle (B) =54^o

a/sinA =b/sinB =c/sinC

a/sin36^o =b/sin54^o =460/sin90^o

a/sin36^o =b/sin54^o =460

a=460sin36^o,b=460sin54^o

a=270,b=372