# Area of Triangle, Sine and Cosine Rules

## Area of Triangle, Sine and Cosine Rules

**Area of a Triangle**

- Understand the formula for
**area of a triangle**given by 1/2 * base * height. - Be aware of the alternate formula for area that uses sides and included angle, represented as 1/2 * a * b * sin(C), where a and b are the lengths of two sides of the triangle and C is the included angle between those sides.
- Apply these concepts to calculate the area of a triangle in various contexts, using either the lengths of the sides or the measure of an included angle.

**Sine Rule**

- Gain proficiency with the
**sine rule**stating that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. - The rule can be written as a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the side lengths and A, B, and C are the angles opposite to these sides respectively in a triangle.
- Use the sine rule to solve problems involving an unknown side length or angle measure in a triangle, providing the ratio of another side to the sine of its opposite angle is known.
- Use the sine rule in the
**ambiguous case**of two possible triangles given certain lengths and angles, known as the**ambiguous case of SSA**.

**Cosine Rule**

- Learn to apply the
**cosine rule**which relates the lengths of the sides of a triangle to the cosine of one of its angles. The rule is usually written as c² = a² + b² - 2ab cos(C), where C is the angle opposite side c. - Use the cosine rule for finding the third side of a triangle when the lengths of two sides and the included angle are known, or to find an angle if all sides are known.
- Recognise when to use the cosine rule based on the information given in the problem.
- Understand the importance of retaining the correct unit of measurement and thus converting units where appropriate when working with the cosine rule.

**Applications of the Sine and Cosine Rules**

- Draw upon the
**sine and cosine rules**to solve a variety of mathematical problems that require finding unknown angles or side lengths in triangles. - Practice contextualising these rules in applied settings, such as physics or engineering problems.
- Remember to check the validity of solutions especially in the ambiguous case with the sine rule.