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 the law of sines

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

Step2: Apply the law of sines

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

Answer:

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