1. The problem is to solve a triangle that is not a right triangle, given one side and one angle. 2. Since it is not a right triangle, we cannot use simple trigonometric ratios like sine, cosine, or tangent directly as with right triangles. 3. To solve such a triangle, you can use the Law of Sines or the Law of Cosines, depending on the data given. 4. The Law of Sines states that $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a, b, c$ are sides and $A, B, C$ are the opposite angles. 5. If you are given one side and one angle not opposite that side, use the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab \cos C$$ for corresponding sides and angles. 6. Steps for Law of Sines approach (given one side and its opposite angle): - Use the given side and angle to find the ratio. - Use the known relationships to find other sides or angles. - Use the triangle angle sum property $A+B+C=180^\circ$ to find the remaining angle. 7. Steps for Law of Cosines approach (given one side and a non-opposite angle): - Use the Law of Cosines formula to find the unknown side. - Apply Law of Sines if necessary to find other angles. - Use triangle angle sum property to find the last angle. 8. Example: Given side $a$ and angle $B$, and you want to find side $b$ and angles $A$ and $C$: - If $a$ is opposite $A$, and knowing angle $B$, use Law of Sines to find side $b$: $$\frac{a}{\sin A} = \frac{b}{\sin B} \Rightarrow b = \frac{a \sin B}{\sin A}$$ - Then use $A+B+C = 180^\circ$ to find $C$. 9. This method enables solving any non-right triangle as long as sufficient data is known.