A triangle has sides a,b,c and angles A,B,C with a opposite A etc. If a=4,b=3,A=40, what is the area of the triangle?

First use the sine rule (that a/sin(A)=b/sin(B)=c/sin(C)) to find the value of B. a/sin(A)=b/sin(B) so B=arcsin(bsin(A)/a) which is approximately equal to 28.82. Since the angles of a triangle have 180 degrees we then know that C is roughly equal to 111.18. Now we can use S=ab*sin(C)/2 where S is the area of the triangle so the area is roughly 5.59.