Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(IGH\), we know \(\sin G=\frac{opposite}{hypotenuse}\). Here, \(\angle G = 61^{\circ}\), the side opposite to \(\angle G\) is \(IH = 2.1\), and the hypotenuse is \(x\).
So, \(\sin61^{\circ}=\frac{2.1}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{2.1}{\sin61^{\circ}}\).
Since \(\sin61^{\circ}\approx0.8746\), then \(x=\frac{2.1}{0.8746}\approx4.8\).

Answer:

$4.8$