Ah...Trigonometry is fun!
The law of sines states:
[tex] \frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c} [/tex]
The transitive property (switching the orders of the equations) applies here. Therfore, we can say that [tex]\frac{sinA}{a}=\frac{sinC}{c} [/tex]
We then plug in our given values to find C
[tex]\frac{sin24}{77}=\frac{sinC}{162} [/tex]
[tex]\frac{162*sin24}{77}=sinC[/tex]
Solving, we get 0.8557316387. We're not done yet!
We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).
arcsin0.8557316387 (arcsin is the same as inverse sin)
=58.8 (approximate)
So the measure of angle C is 58.8. You could check this by reinserting it into the equation [tex] \frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c} [/tex].
:)
