Hello,
1)
Let's put some name of vertex:
A with angle A=45°
B with angle B=90°
C The 3 vertex of the triangle of left.
AC=9 , y=AB=BC
With Pythagore, we can say: y²+y²=9²==>2y²=81===>y=9/√2=9√2/2
The other triangle is BDC: cos(60°)=x/y==>x=y*1/2=9√2/4
2)
Let's give some names:
A with angle A=60°
B with angle B=90
C the 3th vertex of the left triangle.
AB=10, BC=y
tan 60°=y/10=sin(60°)/cos(60°)=(√3/2)/(1/2)=√3==>y=10√3
D is the 3 th vertex of the right triangle.
We use Pythagore: y²+y²=x²
x²=2*(10√3)²===>x=10*√6