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 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 B
8. In ∆CAE, AE = b sin C
9. c sin B = b sin C

Answer 1

In ∆ABD, BD = c sin A

Answer 2

sin x=perpendicular/base