First let's begin by erasing the bad labels and labeling the triangle in standard form. The side opposite vertex A is called a, the side opposite B is called b, and the side opposite C is called c. Here we have a right triangle, C=90 degrees, so a and b are the legs and c the hypotenuse.
The remaining angle B is complementary to A, so B=90-A=90-63=27 degrees.
We're given the hypotenuse c=7, so
[tex]a = c \sin A = 7 \sin 63^\circ \approx 6.327[/tex]
[tex]b = c \cos A = 7 \cos 63^\circ \approx 3.178[/tex]
