Question

find m∠i.
g
6.5
h 3.5 i
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠i = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle GHI \) with \( \angle H = 90^{\circ} \), \( GH = 6.5 \) (opposite to \( \angle I \)) and \( HI = 3.5 \) (adjacent to \( \angle I \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(\angle I)=\frac{GH}{HI}=\frac{6.5}{3.5} \)

Step2: Calculate the angle

First, calculate \( \frac{6.5}{3.5}\approx1.8571 \). Then, to find \( \angle I \), we take the arctangent (inverse tangent) of \( 1.8571 \). Using a calculator, \( \angle I=\arctan(1.8571) \). Calculating this, we get \( \angle I\approx61.8^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 61.8 \)