Warm Up
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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.