Contents

Sine Rule

Solution of Triangle (Sine)

Cosine Rule

Solution of Triangle (Cosine)

Quiz 

Trigonometry Main Page

Solution of Triangle (Cosine)

The Cosine Rule is used in the solution of triangles when two sides and an included angle are given or when three sides are given.

Example 1 (Given three sides)

In triangle ABC, a = 4cm, b = 5cm and c = 7cm. Find the size of the largest angle.

The largest angle is the one facing the longest side, which is angle C.

 

Example 2 (Given two sides and an included angle)

Solve triangle ABC in which ÐA = 55°, b = 2.4cm and and c = 2.9cm

By cosine rule,

a² = 2.4² + 2.9² - 2 x 2.9 x 2.4 cos 55°

    = 6.1858

  a = 2.49cm

 

 

  ÐC = 72.8°, ÐB = 52.2° and a = 2.49cm