Law of Sines and the Ambiguous Case

                     Lesson 1

                                                                                                                                                                          

                                                            Problem:    In ∆FQG, f = 12, q = 10, and m<F = 75.

How many distinct triangles can be drawn given these measurements?

Triangle 5           

                                                            

                                                            Solution     Use the Law of Sines:

Step 1:  f / sin F = q / sin Q                                                                           

                     

                                                            Solution       12/sin75 = 10 / sin Q             

Step 2:                        

                                                                                         

                                                            Solution      12(sin Q) = 10 * sin75            

Step 3:                        

 

                                                            Solution      sin Q = 10 * (1)/12 = 0.8

Step 4:    Angles could be 75, 53.1, and 51.9: sum 180

But, with m<F = 75 and m<Q = 53.1 the sum of the angles

would exceed 180.Not possible! Therefore, m<Q = 51.9, m<f = 75,

and m<Q = 53.1 and only ONE triangle is possible.

 

 

Solution    Answer: only ONE triangle is possible.

Step 5:                                                     

Complete                                                                   

                                                                                                                               

                                                             Try two practice problems:  

 

                                                                                 Solve the following: 

 

From the Above Diagram solve the following:

 

A.

m < F = 24

f = 11

q = 7

B.

m < F = 42

f = 26

y = 9

 

 

                                                                                               

 

 

 

 

 

        

© Math Worksheets World.com