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 \( \triangle EFG \) with \( \angle F = 90^\circ \), \( GF = 2.6 \) (opposite to \( \angle E \)), and \( EF = 7.1 \) (adjacent to \( \angle E \)). We use the tangent function, where \( \tan(\angle E)=\frac{\text{opposite}}{\text{adjacent}}=\frac{GF}{EF} \).

Step2: Calculate the tangent value

Substitute the values: \( \tan(\angle E)=\frac{2.6}{7.1}\approx0.3662 \).

Step3: Find the angle using arctangent

Take the arctangent (inverse tangent) of \( 0.3662 \): \( \angle E=\arctan(0.3662) \). Using a calculator, \( \arctan(0.3662)\approx20.1^\circ \) (rounded to the nearest tenth).

Answer:

\( 20.1 \)