Hello, Shnub!

1) In $\displaystyle \Delta ABC\!:\;\;b = 7,\; a = 12,\;\angle B = 35^o$

. . . Solve the triangle. Code:

A
*
* *
* *
c * * b = 7
* *
* 35° *
B * * * * * * * C
a = 12

Law of Sines: .$\displaystyle \frac{\sin A}{a} \:=\:\frac{\sin B}{b} \quad\Rightarrow\quad \frac{\sin A}{12} \:=\:\frac{\sin35^o}{7}$

. . . . . . . . . . $\displaystyle \sin A \:=\:\frac{12\sin35^o}{7} \;=\;0.983273891$

. . . . . . . . . . $\displaystyle A \;=\;79.50597013^o \quad\Rightarrow\quad \boxed{A \;\approx\;70.5^o}$

Then: .$\displaystyle C \;=\;1870^o - 35^o - 79.5^o \quad\Rightarrow\quad \boxed{C \;=\;65.5^o}$

Law of Sines: .$\displaystyle \frac{c}{\sin C} \:=\:\frac{b}{\sin B} \quad\Rightarrow\quad \frac{c}{\sin65.5^o} \:=\:\frac{7}{\sin35^o}$

. . . . . . . . . . $\displaystyle c \:=\:11.10528343 \quad\Rightarrow\quad \boxed{c \;\approx\;11.1}$