Question

find $m\angle e$.

triangle with right angle at f, fe = 3.2, fg = 8.4, vertices f, e, g

write your answer as an integer or as a decimal rounded to the nearest tenth.
$m\angle e = \square^\circ$

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( EFG \), \( \angle F = 90^\circ \), \( EF = 3.2 \), \( FG = 8.4 \). To find \( m\angle E \), we can use the tangent function: \( \tan(\angle E)=\frac{\text{opposite}}{\text{adjacent}}=\frac{FG}{EF} \).

Step2: Calculate the tangent value

Substitute \( FG = 8.4 \) and \( EF = 3.2 \) into the formula: \( \tan(\angle E)=\frac{8.4}{3.2}=2.625 \).

Step3: Find the angle

Take the arctangent (inverse tangent) of \( 2.625 \) to find \( \angle E \): \( \angle E=\arctan(2.625) \). Using a calculator, \( \arctan(2.625)\approx69.3^\circ \).

Answer:

\( 69.3 \)