Question

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

Explanation:

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

In a triangle, the sum of angles is \( 180^{\circ} \). So, \( \angle D=180^{\circ}-144^{\circ}-19^{\circ}=17^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \). In \( \triangle DEF \), we have \( \frac{e}{\sin E}=\frac{DE}{\sin F} \).
Substituting the values: \( \frac{e}{\sin 19^{\circ}}=\frac{14}{\sin 144^{\circ}} \)
Then \( e=\frac{14\times\sin 19^{\circ}}{\sin 144^{\circ}} \)
We know that \( \sin 19^{\circ}\approx0.326 \), \( \sin 144^{\circ}=\sin(180 - 36)^{\circ}=\sin 36^{\circ}\approx0.588 \)
So \( e=\frac{14\times0.326}{0.588}=\frac{4.564}{0.588}\approx7.8 \)

Answer:

\( 7.8 \)