Triangle Formulae

Maths: Edexcel IGCSE Higher, topic 4.6.4

Area of a Triangle

We can use the formula: area of a triangle = ¹⁄₂ab sin(C).

Formula

Formula

Area of a triangle = ¹⁄₂ab sin(C) since the vertical height is b sin(C).
This formula can also be used to calculate the side length of a triangle whose area is known.

Example

Example

If we are given a triangle with two sides of 8cm and 10cm and the area is 20cm², we can calculate the angle between the sides as follows:
20 = ¹⁄₂ × 8 × 10 × sin(C)
20 = 40 × sin(C)
sin(C) = ¹⁄₂
C = 30°

Sine and Cosine Rules

We can use the sine and cosine rules to calculate angles and lengths in triangles.

Sine rule

Sine rule

Cosine rule

Cosine rule

Labelling triangles

Labelling triangles

Use lowercase letters for the sides and capital letters for the angles opposite each side.

Swapping A, B and C

Swapping A, B and C

Note that the cosine rule can be written for the other angles too:
c² = a² + b² - 2ab cos C
b² = a² + c² - 2ac cos B

Test yourself on Triangle Formulae

Which is the correct formula for the area of a triangle?
What is ${\frac{a}{sin(A)}}$ equal to?
What is ${\frac{c}{sin(C)}}$ equal to?
Would you work out x using the sine or cosine rule?
Would you work out x using the sine or cosine rule?

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