Question

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(DEF\) with \(\angle F = 61^{\circ}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\cos(61^{\circ})=\frac{EF}{DF}\), and \(EF = 11\), \(DF=x\).
So, \(\cos(61^{\circ})=\frac{11}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to get \(x=\frac{11}{\cos(61^{\circ})}\).
We know that \(\cos(61^{\circ})\approx0.4848\).
Then \(x=\frac{11}{0.4848}\approx22.7\).

Answer:

\(22.7\)