Question

practice applying the law of sines. which expression gives the exact value of r? o $\frac{21.3sin(34^{circ})}{sin(118^{circ})}$ o $\frac{sin(34^{circ})}{21.3sin(118^{circ})}$ o $\frac{34sin(118^{circ})}{sin(21.3^{circ})}$ o $\frac{118sin(21.3^{circ})}{sin(34^{circ})}$

Explanation:

Step1: Recall law of sines

The law of sines states that in a triangle $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$, where $a,b,c$ are side - lengths and $A,B,C$ are the opposite angles.
In triangle $STU$, if we assume the side opposite angle $T = 34^{\circ}$ is $t$, the side opposite angle $S=118^{\circ}$ is $s = 21.3$. Then $\frac{t}{\sin T}=\frac{s}{\sin S}$.

Step2: Solve for $t$

Cross - multiply the law of sines formula $\frac{t}{\sin T}=\frac{s}{\sin S}$ to get $t=\frac{s\sin T}{\sin S}$.
Substitute $s = 21.3$, $T = 34^{\circ}$, and $S = 118^{\circ}$ into the formula: $t=\frac{21.3\sin(34^{\circ})}{\sin(118^{\circ})}$.

Answer:

$\frac{21.3\sin(34^{\circ})}{\sin(118^{\circ})}$