Question

Solve triangle ABC

Answer 1

That figure obviously doesn't go with this problem.  It doesn't matter; this is triangle ABC labeled the usual way.

c = 10, B = 35°, C = 65°

We have two angles and a side.  The third angle is obviously

A = 180° -  35°- 65°  = 80°

The remaining sides are given by the Law of Sines,

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

$a = \dfrac{c \sin A}{\sin C} = \dfrac{10 \sin 80}{\sin 65} = 10.866$

$b = \dfrac{c \sin B}{\sin C} = \dfrac{10 \sin 35}{\sin 65} = 6.328$

Answer: A=80°, a=10.9, b=6.3, third choice