Question

find m∠e.
e f
4.6
8
d
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠e = °

Explanation:

Step1: Identify triangle type and sides

Triangle \( EFD \) is right - angled at \( F \). We know that \( EF = 4.6 \) (adjacent to \( \angle E \)) and \( FD=8 \) (opposite to \( \angle E \)). To find \( \angle E \), we can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(\angle E)=\frac{FD}{EF}=\frac{8}{4.6} \).

Step2: Calculate the angle

First, calculate \( \frac{8}{4.6}\approx1.7391 \). Then, to find \( \angle E \), we take the arctangent (inverse tangent) of \( 1.7391 \). Using a calculator, \( \angle E=\arctan(1.7391) \). Calculating this, we get \( \angle E\approx60.1^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 60.1 \)