Given: ∆ABC with AB = c, BC = a, AC = b
Prove: = =

Statement Reason
1. Draw a line through B that is perpendicular to and label the point of intersection with as D. construction
2. In ∆ABD, BD = c sin A definition of sine in right triangle
3. In ∆CBD, BD = a sin C definition of sine in right triangle
4. c sin A = a sin C Substitution Property of Equality
5. = dividing throughout by sin A
sin C
6. Draw a line through A that is perpendicular to and label the point of intersection with as E. construction
7. In ∆BAE, AE = c sin

Question

Given: ∆ABC with AB = c, BC = a, AC = b
Prove:  =  = 

Statement	Reason
1. Draw a line through B that is perpendicular to  and label the point of intersection with as D.	construction
2. In ∆ABD, BD = c sin A	definition of sine in right triangle
3. In ∆CBD, BD = a sin C	definition of sine in right triangle
4. c sin A = a sin C	Substitution Property of Equality
5.  = 	dividing throughout by sin A 
sin C
6. Draw a line through A that is perpendicular to  and label the point of intersection with as E.	construction
7. In ∆BAE, AE = c sin