Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( HGI \), we know angle \( I = 68^\circ \), side \( IG=\sqrt{6} \) (adjacent to angle \( I \)), and we need to find \( HI \) (hypotenuse). We use the cosine function: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So \( \cos(68^\circ)=\frac{IG}{HI} \).

Step2: Solve for \( HI \)

Rearrange the formula: \( HI = \frac{IG}{\cos(68^\circ)} \). Substitute \( IG = \sqrt{6}\approx2.449 \) and \( \cos(68^\circ)\approx0.3746 \). Then \( HI=\frac{2.449}{0.3746}\approx6.5 \).

Answer:

\( 6.5 \)