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

Step2: Substitute known values

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

Step3: Solve for $t$

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

Answer:

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