Cosine Formula

The cosine formula, also known as the law of cosines, is a mathematical formula used to find the length of a side or measure of an angle in a triangle. The formula relates the lengths of the sides of a triangle to the cosine of one of its angles.

The formula is as follows:

c^2 = a^2 + b^2 – 2ab cos(C)

where:

• c is the length of the side opposite to the angle C
• a and b are the lengths of the other two sides
• C is the angle opposite to the side c

Let’s consider an example to see how the cosine formula can be used:

Example: In triangle ABC, side AB has a length of 5 units, side BC has a length of 7 units, and angle ABC measures 60 degrees. Find the length of side AC.

Solution: We can use the cosine formula to find the length of side AC.

c^2 = a^2 + b^2 – 2ab cos(C)

AC^2 = 5^2 + 7^2 – 2(5)(7) cos(60)

AC^2 = 25 + 49 – 70(1/2)

AC^2 = 74 – 35

AC^2 = 39

AC = sqrt(39)

AC ≈ 6.24 units

Therefore, the length of side AC is approximately 6.24 units.