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MAC 1114
Trigonometry Applications : Law of Sines and Cosines Worksheet
Law of Sines (ratio) 𝒔𝒊𝒏 𝑨
𝒂= 𝒔𝒊𝒏 𝑩
𝒃=𝒔𝒊𝒏 𝑪
𝒄
Case 1: given ASA
A = 50o, B = 68o, c = 230.
Hint: angles are usually given in Capital letters and sides in small letters.
1. You can find C. (hint: sum of all angles in a triangle = 180)
2. Set up the ratio using the side given and one of the other angles.
______ = _______ and solve for the missing side.
3. You can repeat this if you need to know all of the sides.
Case 2: given SAA
B = 10o, C = 100o, c = 115
You have enough information to set up a ratio.
_______ = _______ (solving for b); continue if you need to find the other side.
Keep in mind you can find A by using the fact that the sum of all angles in a triangle = 180o.
Case 3: SSA (no solution)
a = 20, c = 45, A = 125o
Set up the ratio to solve for C
______ = ______ ;when you do this you get sin C =1.84 > 1 so outside of the
range for sine values! Therefore, this problem has no solution.
Case 4: given SSA (one solution)
A = 110o, c = 15, a = 28
Set up the ratio for this one using the appropriate ratio.
______ = ______ ; this will give you sin C = .503 or C = 30o or 150o
Let’s try 30o: B = 180 – (110 + 30)= 40oLet’s try 150o: B = 180 – (110 + 150)= -80o X (can’t draw a
triangle with a negative angle) so we reject this one. Thus, there is only one solution to this problem.
When to Use:
ASA and SAA is
given
