Question

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

Explanation:

Step1: Identify triangle type and sides

Triangle \( \triangle NGI \) is right - angled at \( G \). So, \( NG = 4.8 \), \( GI=2.5 \), and we want to find \( m\angle I \). We can use the tangent function, where \( \tan(\angle I)=\frac{\text{opposite}}{\text{adjacent}} \). The side opposite \( \angle I \) is \( NG = 4.8 \), and the side adjacent to \( \angle I \) is \( GI = 2.5 \).

Step2: Apply tangent formula

\( \tan(\angle I)=\frac{NG}{GI}=\frac{4.8}{2.5} = 1.92 \)

Step3: Find the angle

To find \( \angle I \), we take the arctangent (inverse tangent) of \( 1.92 \). So, \( \angle I=\arctan(1.92) \). Using a calculator, \( \arctan(1.92)\approx62.5^\circ \) (rounded to the nearest tenth).

Answer:

\( 62.5 \)