Chapter 8.6, Problem 24WE

To determine

To calculate: prove that in any triangle with acute angles $A$ and $B$ , $\frac{a}{\sin A}=\frac{b}{\sin B}$.

Answer to Problem 24WE

In any triangle with acute angles $A$ and $B$ , $\frac{a}{\sin A}=\frac{b}{\sin B}$ .

Explanation of Solution

Given information: Hint: draw a perpendicular from the third vertex to $\overline{AB}$ label it as p.

Calculation:

Let’s draw a perpendicular from the third vertex to $\overline{AB}$ , and label it as p.

  

Now, from the figure,

  $p=b\sin A=a\sin B,$

  $\Rightarrow \frac{a}{\sin A}=\frac{b}{\sin B}$ . $\square$