Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(IGH\), we know the side opposite the angle \(26^{\circ}\) (\(GH = 6.5\)) and we want to find the hypotenuse (\(x=IG\)). We use the sine ratio. The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(26^{\circ})=\frac{GH}{IG}\).

Step2: Substitute the values and solve for \(x\)

Substitute \(GH = 6.5\) and \(IG=x\) into the sine formula: \(\sin(26^{\circ})=\frac{6.5}{x}\).
We can rewrite this as \(x=\frac{6.5}{\sin(26^{\circ})}\).
Since \(\sin(26^{\circ})\approx0.4384\), then \(x=\frac{6.5}{0.4384}\approx14.8\).

Answer:

\(14.8\)