To solve a triangle is to find the lengths of each of its sides and all its angles.

** ** The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

The cosine rule is used when we are given either

[a] three sides or

[b] two sides and the included angle.

By changing which sides of the triangle play the roles of *a*, *b*, and *c* in the original formula, the following two formulas also state the law of cosines:

To solve a triangle is to find the lengths of each of its sides and all its angles.

** ** The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

The cosine rule is used when we are given either

[a] three sides or

[b] two sides and the included angle.

By changing which sides of the triangle play the roles of *a*, *b*, and *c* in the original formula, the following two formulas also state the law of cosines:

**Skill builder questions**

Practice worksheet – 1 | Angle of any magnitude |

Practice worksheet – 2 | Convert degree – radian |

Practice worksheet – 3 | Measure angle worksheet |

Question no : 1

The radius of a circular oil patch is increasing at a rate of 1.2 cm per minute. Find the rate at which the surface area of the patch is increasing when the radius is 25 cm.