Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(DEF\) with \(\angle D = 22^{\circ}\), \(\text{adjacent side}=DE = 16\) and hypotenuse \(DF=x\). We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(22^{\circ})=\frac{16}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(\cos(22^{\circ})=\frac{16}{x}\) to get \(x=\frac{16}{\cos(22^{\circ})}\).
We know that \(\cos(22^{\circ})\approx0.9272\). Then \(x=\frac{16}{0.9272}\approx17.3\).

Answer:

\(x\approx17.3\)