# The Cosine Rule

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 ab, 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 ab, 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. 