Question

find ( mangle i ).

triangle with vertices h, g, i. right angle at g. side hi is 9.1, side gi is 8.1.

write your answer as an integer or as a decimal rounded to the nearest tenth.

( mangle i = square^circ )

submit

Explanation:

Step1: Identify triangle type and sides

This is a right triangle \( \triangle HGI \) with \( \angle G = 90^\circ \), hypotenuse \( HI = 9.1 \), and side \( GI = 8.1 \). We use the cosine function for \( \angle I \): \( \cos(I)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{GI}{HI} \).

Step2: Calculate cosine of \( \angle I \)

Substitute values: \( \cos(I)=\frac{8.1}{9.1} \approx 0.8901 \).

Step3: Find \( \angle I \)

Take arccosine: \( I=\arccos(0.8901) \approx 27.1^\circ \).

Answer:

\( 27.1 \)