The law of sines is given by the following formula:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
In the question a), we have:
[tex]\begin{gathered} \frac{\sin65°}{31}=\frac{\sin H}{23}\\ \\ \frac{0.90631}{31}=\frac{\sin H}{23}\\ \\ \sin H=\frac{23\cdot0.90631}{31}=0.672423\\ \\ H=42.25° \end{gathered}[/tex]
Rounding to the nearest tenth, we have H = 42.3°.
Now, in question b), we have:
[tex]\begin{gathered} \frac{\sin49°}{23}=\frac{\sin H}{21}\\ \\ \frac{0.75471}{23}=\frac{\sin H}{21}\\ \\ \sin H=\frac{0.75471\cdot21}{23}=0.689083\\ \\ H=43.56° \end{gathered}[/tex]
Rounding to the nearest tenth, we have H = 43.6°.
