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 trigonometric ratio

This is a right - triangle \( \triangle HGI \) with \( \angle G = 90^{\circ} \), \( HG = 4.5 \), and \( IG=8.3 \). To find \( \angle I \), we can use the tangent function. The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For \( \angle I \), the opposite side is \( HG = 4.5 \) and the adjacent side is \( IG = 8.3 \). So, \( \tan(\angle I)=\frac{HG}{IG}=\frac{4.5}{8.3} \).

Step2: Calculate the angle

We need to find the angle whose tangent is \( \frac{4.5}{8.3} \). Using a calculator, we first calculate \( \frac{4.5}{8.3}\approx0.5422 \). Then, we find the arctangent (inverse tangent) of \( 0.5422 \). \( \angle I=\arctan(0.5422) \). Using a calculator in degree mode, \( \arctan(0.5422)\approx28.4^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 28.4 \)