Question

find the sine of ∠e. write your answer in simplified, rationalized form. do not round. sin(e) =

Explanation:

Step1: Find length of FG

In right triangle \( FGE \), by Pythagorean theorem \( FG^2 + EG^2 = EF^2 \). Given \( EF = 10 \), \( EG=\sqrt{86} \), so \( FG^2=10^2 - (\sqrt{86})^2 = 100 - 86 = 14 \), thus \( FG = \sqrt{14} \).

Step2: Calculate \( \sin(E) \)

In right triangle, \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). For \( \angle E \), opposite side is \( FG=\sqrt{14} \), hypotenuse is \( EF = 10 \). So \( \sin(E)=\frac{\sqrt{14}}{10} \).

Answer:

\(\frac{\sqrt{14}}{10}\)