Warm Up

Warm UpConsider triangle SJT. Side s = 49, side j = 16,

and angle S = 115°. Find all unknowns.

Example 4

Solve ΔLMN given that l = 13, m = 8, and angle L = 38.8°.

L = _____ M = _____ N = _____l = _____ m = _____ n = _____

Example 5

Solve ΔPQR given that q = 16, r = 21, and angle Q = 82.1°.

P = _____ Q = _____ R = _____p = _____ q = _____ r = _____

LAW OF COSINES

Remember how we need buddies to use the Law of Sines?

In order to use the Law of Sines, we need a side and its corresponding angle to apply to the ratio.

What if we don’t have buddies?

Law of Cosines!Let ΔABC be any triangle with angles A, B, and C

opposite sides a, b, and c, respectively, then following equations are true:

a2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C

Note that each equation has one

angle each. Therefore, we decide which equation to use by using the angle we have (or the angle we

want to find!).

Example 1

Solve ΔABC given that a = 11, b = 5, and angle C = 20°.

Example 2

Solve ΔABC if a = 9, b = 7, and c = 5.