Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( HIJ \), we know angle \( H = 66^\circ \), side \( IJ = 9 \) (opposite to angle \( H \)), and we need to find \( HI \) (adjacent to angle \( H \)). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(66^\circ)=\frac{IJ}{HI} \).

Step2: Solve for \( HI \)

Rearranging the formula, \( HI = \frac{IJ}{\tan(66^\circ)} \). Substitute \( IJ = 9 \) and \( \tan(66^\circ) \approx 2.246 \). Then \( HI=\frac{9}{2.246}\approx 4.0 \) (rounded to the nearest tenth).

Answer:

\( 4.0 \)