Question

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

Explanation:

Step1: Identify triangle type and law

This is a triangle with angles \(36^\circ\), \(30^\circ\), and side \(6\) opposite \(36^\circ\), side \(e\) opposite \(30^\circ\). Use the Law of Sines: \(\frac{e}{\sin 30^\circ}=\frac{6}{\sin 36^\circ}\).

Step2: Solve for \(e\)

Rearrange the formula: \(e = \frac{6 \times \sin 30^\circ}{\sin 36^\circ}\). We know \(\sin 30^\circ = 0.5\) and \(\sin 36^\circ \approx 0.5878\). Substitute values: \(e=\frac{6\times0.5}{0.5878}=\frac{3}{0.5878}\approx5.1\).

Answer:

\(e \approx 5.1\)