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11/3: Apply the Law of Sines to find missing side lengths and angle measures for any triangle. Do Now On your desk: - Pencil & Calculator -Today’s Handouts DO NOW! Agenda DO NOW! & Check Guided Notes Independent Practice Homework! (maybe…) Homework Handout (8 problems) Unit 1 Test MONDAY 11/14! Start studying now!

We will learn to… Apply Law of Sines to find missing side lengths and angle measures of any triangle.

Law of Sines: sin a A sin b B sin c C = = b a A C B c sin a A sin b B sin c C = = side lengths Law of Sines is used to find missing _____________________ when you are given _______________ and _________________. It can also be used to find missing _____________________ when you are given _______________ and _________________. two angles one side angle measures two sides one angle

Example 1: Find the value of A. Round to nearest tenth. b Given: Write Equation, Substitute, & Solve: NOT Right Triangle! sin a A sin b B sin c C C 39° = = 45° A 6 Angle a = 45° Angle b = 39° a Side B = 6 sin 45° A sin 39° 6 c = B Finding: A sin 45° 6 Side A = sin 39° A sin 45° Law of Sines?: *sin 45° = 9.534 *sin 45° Yes! A = 9.534 *sin 45° A ≈ 6.7 units

Example 2: Find the value of c. Round to nearest tenth. Given: b Write Equation, Substitute, & Solve: NOT Right Triangle! sin a A sin c C C sin b B 70° A 9 = = 7 Angle b = 70° Side B = 9 Side C = 7 a sin 70° 9 sin c 7 c = B Finding: sin c 7 Angle c 7* 0.104 = *7 Law of Sines?: 0.731 = sin c Yes! sin-1(0.731) = c 46.959° c = c ≈ 47°

Example 3: Find the area of the triangle. Round to tenth. Given: b Write Equation, Substitute, & Solve: NOT Right Triangle! C * side 1 sin θ 2 * side 2 Area = A 9 Angle c = 47° 6 Side A = 6 Side B = 9 a 47° * 6 sin 47° 2 * 9 c Area = B Finding: Area of Triangle Area ≈ 19.7 units2 Law of Sines?: Yes! (kinda sorta…)