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) =
2. multiply both sides of the equation by c and simplify. the equation sin(b) = $\frac{h}{c}$ becomes c sin(b)=h.
3. for △acd, sin(c) =

Explanation:

Step1: Recall sine - definition in right - triangle

In right - triangle $\triangle ACD$, the sine of an angle is the ratio of the opposite side to the hypotenuse.

Step2: Identify opposite and hypotenuse for $\angle C$

In $\triangle ACD$, the side opposite to $\angle C$ is $h$ and the hypotenuse is $b$. So, $\sin(C)=\frac{h}{b}$.

Answer:

$\frac{h}{b}$