1. 11/3: Apply the Law of Sines to find missing side lengths and angle measures for any triangle.
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- Pencil & Calculator
-Today’s Handouts
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Agenda
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Guided Notes
Independent Practice
Homework! (maybe…)
Homework
Handout
(8 problems)
Unit 1 Test MONDAY 11/14!
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2. We will learn to…
Apply Law of Sines to find missing side lengths and angle measures of any triangle.

3. 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

4. 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 ≈ units

5. 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°

6. 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 ≈ units2
Law of Sines?:
Yes! (kinda sorta…)