Question

which equation is true for triangle qrs? law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Recall law of sines

The law of sines states that in a triangle $\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}$, where $A$, $B$, $C$ are angles and $a$, $b$, $c$ are the lengths of the sides opposite to those angles respectively. In $\triangle QRS$, angle $R = 100^{\circ}$, the side opposite to angle $R$ is $q = 3.5$, the side opposite to angle $S$ is $r=2.4$.

Step2: Apply law of sines

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

Answer:

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