Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(IGH\), we know the side adjacent to angle \(G\) (\(GH = 2.1\)) and we want to find the hypotenuse (\(IG=x\)). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 61^{\circ}\), adjacent side \(a = 2.1\), and hypotenuse \(c=x\). So, \(\cos(61^{\circ})=\frac{2.1}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(\cos(61^{\circ})=\frac{2.1}{x}\) to get \(x=\frac{2.1}{\cos(61^{\circ})}\).
We know that \(\cos(61^{\circ})\approx0.4848\). Then \(x=\frac{2.1}{0.4848}\).

$$x=\frac{2.1}{0.4848}\approx4.3$$

Answer:

\(x\approx4.3\)