Sine Rule, Cosine Rule, Area of a Triangle

What are the formulas for sine rule, cosine rule, and area of a triangle?

In this post, we establish and use the sine rule, cosine rule, and the area of a triangle formula for solving problems where angles are measured in degrees, or degrees and minutes, as a part of the Prelim Maths Advanced course under the topic Trigonometric Functions and sub-part Trigonometry. The sine rule and cosine rule are formulas that can be used to assist you in finding the unknown side or angle of a triangle when given enough information.

Sine Rule: $\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}$
Cosine Rule: $c^{2} = a^{2} + b^{2} - 2 a b cos(C)$

The area of a triangle is: $A = \frac{1}{2} b h$ , however, this is only for right-angled triangles, if the triangle does not involve a right angle, the formula is: $A = \frac{1}{2} a b sin(C)$ .

What is the sine rule?

The following two videos cover the topic of the sine rule, explaining it in detail in the first video, and proving and using the formula in examples in the second video.

Part 1

Part 2

What is the Cosine Rule?

The following three videos cover the topic of the cosine rule. The first video videos a logical explanation of the proof of the formula, the second video gives a basic example of how to find the unknown side in a triangle, while the last gives a great explanation on when to use the cosine rule as opposed to the sine rule.