Question

which equation is true for triangle qrs? law of sines: sina/a = sinb/b = sinc/c o sin(120°)/3.5 = sin(s)/2.4 o sin(120°)/3.5 = sin(q)/2.4 o sin(120°)/2.4 = sin(s)/3.5 o sin(120°)/2.4 = sin(q)/3.5

Explanation:

Step1: Recall the law of sines

The law of sines states that in a triangle $\triangle ABC$ with sides $a$, $b$, $c$ and opposite - angles $A$, $B$, $C$ respectively, $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$. In $\triangle QRS$, let the angle at $R = 100^{\circ}$, the side opposite to $R$ be $q = 3.5$, the side opposite to $Q$ be $r = 2.4$.

Step2: Apply the law of sines

According to the law of sines, $\frac{\sin R}{q}=\frac{\sin Q}{r}$. Substituting $R = 100^{\circ}$, $q = 3.5$ and $r = 2.4$, we get $\frac{\sin(100^{\circ})}{3.5}=\frac{\sin(Q)}{2.4}$.

Answer:

$\frac{\sin(100^{\circ})}{3.5}=\frac{\sin(Q)}{2.4}$ (the first option)