Question

I need help finding the missing sides using the law of sines

Answer 1

Check the picture below.

Answer 2

By the law of sines,

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

The interior angles of any triangle sum to 180 degrees in measure, so we know

$m\angle A=(180-85-40)^\circ=55^\circ$

Then

$\dfrac{\sin55^\circ}a=\dfrac{\sin85^\circ}{26}\implies a\approx21$

and

$\dfrac{40^\circ}c=\dfrac{\sin85^\circ}{26}\implies c\approx17$