Answer:
Sam = 18 and Marlon = 12
Step-by-step explanation:
If Sam is 6 years older but added is 30 then Sam could 18 and Marlon 12.
We know that the law of sines states that:
![\frac{\sin\alpha}{a}=\frac{\sin\beta}{b}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%5Calpha%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%5Cbeta%7D%7Bb%7D)
For simplicity, let:
![\beta=m\angle A_1BC](https://tex.z-dn.net/?f=%5Cbeta%3Dm%5Cangle%20A_1BC)
In triangle A1BC this leads to:
![\begin{gathered} \frac{\sin31}{5}=\frac{\sin\beta}{6} \\ \sin\beta=\frac{6}{5}\sin31 \\ \beta=\sin^{-1}(\frac{6}{5}\sin31) \\ \beta=38.174 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%5Csin31%7D%7B5%7D%3D%5Cfrac%7B%5Csin%5Cbeta%7D%7B6%7D%20%5C%5C%20%5Csin%5Cbeta%3D%5Cfrac%7B6%7D%7B5%7D%5Csin31%20%5C%5C%20%5Cbeta%3D%5Csin%5E%7B-1%7D%28%5Cfrac%7B6%7D%7B5%7D%5Csin31%29%20%5C%5C%20%5Cbeta%3D38.174%20%5Cend%7Bgathered%7D)
Therefore:
![m\angle A_1BC=38.174](https://tex.z-dn.net/?f=m%5Cangle%20A_1BC%3D38.174)
Now, triangle A2BC is isosceles which means that both the base angles are equal, since angle CA1B and A2A1B are supplementary we have: