9-3 Law of Sines

Law of Sines is only used when the triangle is not a right triangle.
You use Law of Sines when the triangle has an angle and it's opposite leg.
When you use the inverse, you will get two answers.

Formula: SinA/a = SinB/b = SinC/c

Ex. 1 Triangle ABC gives you angle A, angle B, angle C, and leg a. Angle A = 80, angle B = 25, angle C = 75, and leg a = 10. Solve the triangle.

• First, you need to see which angle has an opposite side: angle A and leg a are opposite sides. You will use this angle and leg to find the other legs.
  
• Second, you need to pick one of the legs to find (doesn't matter which one). To find leg b: Sin80/10=Sin25/b. bSin80=10sin25. b=10Sin25/Sin80. b = 4.291
• Now find leg c: Sin80/10=Sin75/c. cSin80=10Sin75. c=10Sin75/Sin80. c = 9.808

Ex.2 Triangle ABC gives you angle B, leg a, and leg b. Angle B = 28, leg a = 7, and leg b = 3. Solve the triangle.

• First, find out if angle B has an opposite side: It does. Leg b is its opposite side.
• Second, since you do not have any other angle besides angle B, you have to find the other angles first: Sin28/3=SinA/7 (use angle A because it gave you leg a which is opposite from angle A). 3SinA=7Sin28. (take the inverse of sin) B=sin^-1(7Sin28/3). B = .019
• Now find angle C: 180-28-.019 = 151.981
• After you find angle C, you can now find leg c: Sin28/3=Sin151.981/c. cSin28=3Sin151.981. c=3Sin151.981/Sin28. c = 3.002