4.6. Law of Sines http://www.ck12.org
Guided Practice
- Given∆ABCwhereA= 10 ◦,b= 10 ,a=11, find^6 B.
- Given∆ABCwhereA= 12 ◦,B= 50 ◦,a=14 findb.
- Given∆ABCwhereA= 70 ◦,b= 8 ,a=3, find^6 Bif possible.
Answers:
1.sin^10 B=sin 10^11 ◦
B=sin−^1 (10 sin 10 11 ◦)≈ 9. 08 ...◦
2.sin 12^14 ◦=sin 50b ◦
b=14 sin 50sin 12◦◦≈ 51. 58 ...
- sin 70◦=h 8
h=8 sin 70◦≈ 7. 51 ...
Becausea<h, this triangle is impossible.
Practice
For 1-3, draw a picture of the triangle and state how many triangles could be formed with the given values.
1.A= 30 ◦,a= 13 ,b= 15
2.A= 22 ◦,a= 21 ,b= 12
3.A= 42 ◦,a= 36 ,b= 37
For 4-7, find all possible measures of^6 B(if any exist) for each of the following triangle values.
4.A= 86 ◦,a= 15 ,b= 11
5.A= 30 ◦,a= 24 ,b= 43
6.A= 48 ◦,a= 34 ,b= 39
7.A= 80 ◦,a= 22 ,b= 20
For 8-12, find the length ofbfor each of the following triangle values.
8.A= 94 ◦,a= 31 ,B= 34 ◦
9.A= 112 ◦,a= 12 ,B= 15 ◦
10.A= 78 ◦,a= 20 ,B= 16 ◦
11.A= 54 ◦,a= 15 ,B= 112 ◦
12.A= 39 ◦,a= 9 ,B= 98 ◦
- In∆ABC,b=10 and^6 A= 39 ◦. What’s a possible value forathat would produce two triangles?
- In∆ABC,b=10 and^6 A= 39 ◦. What’s a possible value forathat would produce no triangles?
- In∆ABC,b=10 and^6 A= 39 ◦. What’s a possible value forathat would produce one triangle?