Question

31.
25
$x^circ$
$119^circ$
13
$x =$

Explanation:

Step1: Apply Law of Sines

$\frac{\sin x}{13} = \frac{\sin 119^\circ}{25}$

Step2: Isolate $\sin x$

$\sin x = \frac{13 \times \sin 119^\circ}{25}$

Step3: Calculate $\sin 119^\circ$

$\sin 119^\circ = \sin(61^\circ) \approx 0.8746$

Step4: Compute numerator

$13 \times 0.8746 \approx 11.37$

Step5: Solve for $\sin x$

$\sin x \approx \frac{11.37}{25} \approx 0.4548$

Step6: Find $x$ via arcsine

$x \approx \arcsin(0.4548) \approx 27^\circ$

Answer:

$x \approx 27^\circ$