Question

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

Explanation:

Step1: Identify triangle type and sides

Triangle \( FDE \) is right - angled at \( D \). Hypotenuse \( FE = 10 \), adjacent side to \( \angle E \) is \( DE = 4 \). We can use the cosine function, where \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle E \), \( \cos(\angle E)=\frac{DE}{FE}=\frac{4}{10} = 0.4 \).

Step2: Find the angle

To find \( \angle E \), we take the inverse cosine (arccos) of \( 0.4 \). Using a calculator, \( \angle E=\arccos(0.4)\approx66.4^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 66.4 \)