You didn't state which problem you need help with, so I will solve problem #1 and #2. (If you need a different problem, state so in the comments).
The Law of Sines is a proportion: [tex]\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}[/tex] : where A, B, C is the angle and a, b, c are the corresponding sides.
1)
[tex]\frac{sin50}{23}= \frac{sin76}{b}[/tex] Set up the proportion
(sin 50)*b = (sin 76)*23 cross multiply
b = (sin 76)*23 ÷ (sin 50) isolate the variable
b = 29.13 use calculator to simplify
2)
[tex]\frac{sin102}{35} = \frac{sin40}{s}[/tex] Set up the proportion
(sin 102)*s = (sin 40)*35 cross multiply
s = (sin 40)*35 ÷ (sin 102) isolate the variable
s = 23 use calculator to simplify
