Question

ivan began to prove the law of sines using the diagram and equations below.$sin(a) = h/b$, so $b sin(a) = h$.$sin(b) = h/a$, so $a sin(b) = h$.therefore, $b sin(a) = a sin(b)$.which equation is equivalent to the equation $b sin(a) = a sin(b)$?$\bigcirc$ $\frac{a}{sin(b)} = \frac{b}{sin(a)}LXB0\bigcirc$ $\frac{sin(a)}{sin(b)} = \frac{b}{a}$$\bigcirc$ $\frac{sin(b)}{a} = \frac{sin(a)}{b}$

Explanation:

Step1: Divide both sides by $\sin(A)\sin(B)$

Starting with $b \sin(A) = a \sin(B)$, divide each term by $\sin(A)\sin(B)$:
$$\frac{b \sin(A)}{\sin(A)\sin(B)} = \frac{a \sin(B)}{\sin(A)\sin(B)}$$
Simplify to get:
$$\frac{b}{\sin(B)} = \frac{a}{\sin(A)}$$

Step2: Rearrange terms for matching option

Swap the left and right sides, then rewrite to match the form of the options:
$$\frac{a}{\sin(B)} = \frac{b}{\sin(A)}$$

Answer:

A. $\frac{a}{\sin(B)} = \frac{b}{\sin(A)}$