Question

proving the law of sines
two right triangles, △abd and △acd, were created from △abc by constructing ad ⊥ cb.
follow these steps to prove that $\frac{sin(b)}{b}=\frac{sin(c)}{c}$.

1. for △abd, sin(b) =

Explanation:

Step1: Recall sine - definition in right - triangle

In right - triangle $\triangle ABD$, the sine of an angle in a right - triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For $\angle B$ in $\triangle ABD$, the opposite side to $\angle B$ is $AD$ (denoted as $h$) and the hypotenuse is $c$.
So, $\sin(B)=\frac{h}{c}$.

Answer:

$\frac{h}{c}$