Question

find e.
write your answer as an integer or as a decimal rounded to the nearest tenth.
e =
submit
work it out
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Explanation:

Step1: Find the measure of angle \( F \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( \angle F=180^{\circ}-(108^{\circ} + 29^{\circ})=43^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{e}{\sin E}=\frac{EF}{\sin G} \). Here, \( EF = 8 \), \( \angle E=108^{\circ} \), \( \angle G = 29^{\circ} \).
So, \( e=\frac{8\times\sin108^{\circ}}{\sin29^{\circ}} \)
Since \( \sin108^{\circ}\approx0.9511 \), \( \sin29^{\circ}\approx0.4848 \)
\( e=\frac{8\times0.9511}{0.4848}\approx15.7 \)

Answer:

\( 15.7 \)