Chapter 6.1, Problem 1E

To determine

Fill in the blanks:

Law of sign: $\frac{a}{\sin A}=\_\_\_\_\_=\frac{c}{\sin C}$

Answer to Problem 1E

Law of sign: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Explanation of Solution

In case $ABC$ is a triangle with sides $a,b,c$ then $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ .

Therefore, by laws of sign,

  $\frac{b}{\sin B}$

Thus, Law of sign: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$