Question

find m∠e.

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

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle EFD \) with \( \angle F = 90^\circ \), \( EF = 5.4 \), and \( ED = 6.5 \). To find \( m\angle E \), we can use the cosine ratio since \( \cos(\angle E)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{EF}{ED} \).

Step2: Calculate the cosine value

Substitute the values: \( \cos(\angle E)=\frac{5.4}{6.5}\approx0.8308 \).

Step3: Find the angle using inverse cosine

Take the inverse cosine: \( \angle E=\cos^{-1}(0.8308) \). Using a calculator, \( \angle E\approx33.8^\circ \) (rounded to the nearest tenth).

Answer:

\( 33.8 \)