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Warm Up

Warm Up. Consider 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.

dean-richard
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Warm Up

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  1. Warm Up Consider triangle SJT. Side s = 49, side j = 16, and angle S = 115°. Find all unknowns.

  2. Example 4 Solve ΔLMN given that l = 13, m = 8, and angle L = 38.8°. L = _____ M = _____ N = _____ l = _____ m = _____ n = _____

  3. Example 5 Solve ΔPQR given that q = 16, r = 21, and angle Q = 82.1°. P = _____ Q = _____ R = _____ p = _____ q = _____ r = _____

  4. Law of Cosines

  5. 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?

  6. 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!).

  7. Example 1 Solve ΔABC given that a = 11, b = 5, and angle C = 20°.

  8. Example 2 Solve ΔABC if a = 9, b = 7, and c = 5.

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