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 \(HIJ\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 51^{\circ}\), the opposite side to \(\angle I\) is \(HJ\) and the hypotenuse is \(HI\), and \(IJ = 4\). So, \(\sin(51^{\circ})=\frac{IJ}{HI}\).

Step2: Solve for \(HI\)

We can rewrite the formula as \(HI=\frac{IJ}{\sin(51^{\circ})}\). Since \(\sin(51^{\circ})\approx0.777\) and \(IJ = 4\), then \(HI=\frac{4}{\sin(51^{\circ})}\approx\frac{4}{0.777}\approx5.2\).

Answer:

$5.2$