Determine the value of A ​

Draw XY.

This creates right triangle(WXY).

By the Pythagorean theorem, WY  =  4·sqrt(2).

Since triangle(WXY) is an isosceles right triangle, angle(XYW) = 45^o.

This makes angle(ZYW) = 90^o.

Use the Pythagorean Theorem:  WZ²  =  WY² + YZ².

--->     9²  =  [ 4·sqrt(2) ]² + a²

 

Finish this to get the answer ...