Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Calculate $\angle F$

The sum of angles in a triangle is $180^\circ$.
$\angle F = 180^\circ - 26^\circ - 30^\circ = 124^\circ$

Step2: Find side $g$ via Law of Sines

Relate $g$, $\angle G$, side 13, $\angle F$.
$\frac{g}{\sin 30^\circ} = \frac{13}{\sin 124^\circ}$
$g = \frac{13 \times \sin 30^\circ}{\sin 124^\circ} = \frac{13 \times 0.5}{\sin 124^\circ} \approx \frac{6.5}{0.8290} \approx 7.8$

Step3: Find side $h$ via Law of Sines

Relate $h$, $\angle H$, side 13, $\angle F$.
$\frac{h}{\sin 26^\circ} = \frac{13}{\sin 124^\circ}$
$h = \frac{13 \times \sin 26^\circ}{\sin 124^\circ} \approx \frac{13 \times 0.4384}{0.8290} \approx \frac{5.70}{0.8290} \approx 6.9$

Answer:

$\angle F = 124^\circ$, $g \approx 7.8$, $h \approx 6.9$