#1
[tex]sin(51^o)= \frac{y}{12} \ \ \to \ \ y=12*sin(51^o)=12* 0.7771 \approx 9.33[/tex]
#2
[tex]\theta=arccos( \frac{5^2+13^2-12^2}{2*5*13}) = arccos( \frac{25+169-144}{130})=arccos( \frac{50 }{130})= \\ \\ arccos(0.3846) \approx67.4^o[/tex]
#3
[tex]tan(13^o)= \frac{x}{24} \ \ \to \ \ x=24*tan(13^o)=24* 0.2309 \approx 5.54[/tex]
#4
[tex]sin(20^o)= \frac{10}{x} \ \ \to \ \ x= \frac{10}{sin(20^o)} = \frac{10}{0.342} \approx 29.24[/tex]
