Question

unit exam - right triangles and trigonometry
solve for x.
8
7
$x = \boldsymbol{?}^\circ$
law of sines: $\frac{\sin a}{a} = \frac{\sin b}{b} = \frac{\sin c}{c}$
round your answer to the nearest hundredth.

Explanation:

Step1: Apply Law of Sines

$\frac{\sin(43^\circ)}{7} = \frac{\sin(x^\circ)}{8}$

Step2: Isolate $\sin(x^\circ)$

$\sin(x^\circ) = \frac{8 \times \sin(43^\circ)}{7}$

Step3: Calculate numerator value

$\sin(43^\circ) \approx 0.6820$, so $8 \times 0.6820 = 5.456$

Step4: Compute $\sin(x^\circ)$

$\sin(x^\circ) = \frac{5.456}{7} \approx 0.7794$

Step5: Find $x$ via arcsine

$x = \arcsin(0.7794) \approx 51.25^\circ$

Answer:

$51.25$