Non-right-angled triangles can be a bit tougher to work with than right-angled triangles. The main reason is that the sides and angles in these triangles are more complicated.

In right-angled triangles, we can easily use basic trigonometric ratios like sine, cosine, and tangent. Here’s what they mean:

• Sine: $\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}}$
• Cosine: $\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}}$
• Tangent: $\tan(A) = \frac{\text{opposite}}{\text{adjacent}}$

But for non-right-angled triangles, we need some special rules to help us figure out the sides and angles. The two main rules are:

1. Sine Rule: This rule is useful for any triangle. If you have angles $A$, $B$, and $C$, and sides $a$, $b$, and $c$, the Sine Rule says:

   $$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$

   This means you can find unknown sides or angles if you know some other sides or angles.

2. Cosine Rule: The Cosine Rule connects the lengths of the sides to the cosine of one angle. It looks like this:

   $$c^2 = a^2 + b^2 - 2ab \cos(C)$$

   This rule is really helpful when you know two sides and the angle between them or when you know all three sides and want to find an angle.

It's important for Year 12 students to understand these rules well. Non-right-angled triangle problems come up a lot in tests. In fact, about 30% of the geometry and trigonometry questions in AS-Level math tests focus on these rules. So, mastering these concepts is really important for doing well!