Question

find g.
write your answer as an integer or as a decimal rounded to the nearest tenth.
g =
submit

Explanation:

Step1: Find angle at E

In triangle \( EFG \), the sum of interior angles is \( 180^\circ \). So, \( \angle E = 180^\circ - 83^\circ - 68^\circ = 29^\circ \).

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{g}{\sin G} = \frac{EG}{\sin F} \). We know \( EG = 14 \), \( \angle G = 83^\circ \), \( \angle F = 68^\circ \). So, \( g = \frac{14 \times \sin 83^\circ}{\sin 68^\circ} \).
Calculate \( \sin 83^\circ \approx 0.9925 \), \( \sin 68^\circ \approx 0.9272 \). Then \( g = \frac{14 \times 0.9925}{0.9272} \approx \frac{13.895}{0.9272} \approx 14.9 \).

Answer:

\( 14.9 \)