Question

use the law of sines. find the measure x to the nearest tenth.

Explanation:

Step1: Find angle A

First, calculate $\angle A$ using the triangle angle sum (total $180^\circ$).
$\angle A = 180^\circ - 80^\circ - 57^\circ = 43^\circ$

Step2: Apply Law of Sines

Set up the Law of Sines proportion for side $x$ (side AB) and side BC (length 7).
$\frac{x}{\sin(80^\circ)} = \frac{7}{\sin(43^\circ)}$

Step3: Solve for x

Rearrange to isolate $x$, then compute the value.
$x = \frac{7 \times \sin(80^\circ)}{\sin(43^\circ)}$
Calculate the sines: $\sin(80^\circ) \approx 0.9848$, $\sin(43^\circ) \approx 0.6820$
$x \approx \frac{7 \times 0.9848}{0.6820} \approx \frac{6.8936}{0.6820} \approx 10.1$

Answer:

10.1