Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(IGH\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 48^{\circ}\), the adjacent side to \(\theta\) is \(IH = 4.5\), and the hypotenuse is \(IG=x\). So, \(\cos48^{\circ}=\frac{4.5}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(\cos48^{\circ}=\frac{4.5}{x}\) to get \(x=\frac{4.5}{\cos48^{\circ}}\).
We know that \(\cos48^{\circ}\approx0.6691\). Then \(x=\frac{4.5}{0.6691}\approx6.7\).

Answer:

\(6.7\)