Question

solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(IGH\), we know the adjacent side (\(IH = 4.5\)) to the angle \(48^{\circ}\) and we need to find the hypotenuse (\(x\)). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(48^{\circ})=\frac{IH}{x}\).

Step2: Solve for \(x\)

Since \(\cos(48^{\circ})=\frac{4.5}{x}\), we can re - arrange the formula to \(x = \frac{4.5}{\cos(48^{\circ})}\).
We know that \(\cos(48^{\circ})\approx0.6691\). Then \(x=\frac{4.5}{0.6691}\approx6.7\).

Answer:

\(6.7\)