need help with geometry

There is a nice formula that you can use to calculate the area of a triangle:  Area  =  ½·a·b·sin(C)

where a and b are two sides and C is the angle between those sides.

 

We could use that formula for this problem if we knew the length of side WY.

 

We could use the Law of Sines to find WY if we knew the size of angle(X).

 

Step 1:  Find the size of angle(X)   --->   angle(X) = 180^o - 27^o - 40^o  =  ........

 

Step 2:  Use the result of Step 1 to find WY  --->  WY / sin(X)  =  WX / sin(Y)

                     --->   WY / sin(X)  =  38 / sin( 40^o )   

                     --->  WY  =  38 / sin( 40^o ) · sin(X)  =  ........

 

Step 3:  Find the area:  Area  =  ½ · WX · WY · sin( angle(W) )

                     --->   Area  =  ½ · 38 · WY · sin( 27^o )  =  .......