Question

find g.
write your answer as an integer or as a decimal rounded to the nearest tenth.
g =
submit
work it out
not feeling ready

Explanation:

Step1: Find angle at F

In triangle \( EFG \), the sum of angles is \( 180^\circ \). So \( \angle F = 180^\circ - 32^\circ - 80^\circ = 68^\circ \).

Step2: Apply Law of Sines

Law of Sines: \( \frac{g}{\sin G} = \frac{FG}{\sin E} \). Here, \( FG = 8 \), \( \angle G = 80^\circ \), \( \angle E = 32^\circ \). So \( g = \frac{8 \times \sin 80^\circ}{\sin 32^\circ} \).
Calculate \( \sin 80^\circ \approx 0.9848 \), \( \sin 32^\circ \approx 0.5299 \). Then \( g \approx \frac{8 \times 0.9848}{0.5299} \approx \frac{7.8784}{0.5299} \approx 14.9 \).

Answer:

\( 14.9 \)