Question

find ij.
triangle image with right angle at j, angle at h is 54°, length of hj is 4.4
write your answer as an integer or as a decimal rounded to the nearest tenth.
ij =
submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( IJH \), we know angle \( H = 54^\circ \), side \( HJ = 4.4 \) (adjacent to angle \( H \)), and we need to find \( IJ \) (opposite to angle \( H \)). The tangent ratio is \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(54^\circ)=\frac{IJ}{HJ} \).

Step2: Solve for \( IJ \)

Substitute \( HJ = 4.4 \) and \( \theta = 54^\circ \) into the formula: \( IJ = HJ\times\tan(54^\circ) \). Calculate \( \tan(54^\circ)\approx1.3764 \), then \( IJ = 4.4\times1.3764 \approx 6.1 \).

Answer:

\( 6.1 \)