Question

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

Explanation:

Step1: Recall Law of Sines

For $\triangle STU$, $\frac{t}{\sin(\angle T)} = \frac{SU}{\sin(\angle S)}$

Step2: Substitute known values

$\angle T=34^\circ$, $\angle S=118^\circ$, $SU=21.3$, so:
$\frac{t}{\sin(34^\circ)} = \frac{21.3}{\sin(118^\circ)}$

Step3: Solve for $t$

Rearrange to isolate $t$:
$t = \frac{21.3\sin(34^\circ)}{\sin(118^\circ)}$

Answer:

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