Question

find ( mangle e ).

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle e = square^circ )

Explanation:

Step1: Identify triangle type and sides

Triangle \( CDE \) is right - angled at \( D \). We know that \( ED = 3.4 \) (adjacent to \( \angle E \)) and \( CD = 2.4 \) (opposite to \( \angle E \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle E \), \( \tan(\angle E)=\frac{CD}{ED} \).

Step2: Calculate the tangent value

Substitute the values of \( CD = 2.4 \) and \( ED = 3.4 \) into the tangent formula: \( \tan(\angle E)=\frac{2.4}{3.4}\approx0.7059 \).

Step3: Find the angle

To find \( \angle E \), we take the arctangent (inverse tangent) of \( 0.7059 \). Using a calculator, \( \angle E=\arctan(0.7059) \). Calculating this, we get \( \angle E\approx35.2^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 35.2 \)