Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(NML\), \(\angle N = 46^{\circ}\), hypotenuse \(NL = 4.1\), and we want to find the adjacent side \(x\) (adjacent to \(\angle N\)). We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos(46^{\circ})=\frac{x}{4.1}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(46^{\circ})=\frac{x}{4.1}\) by \(4.1\).
We know that \(\cos(46^{\circ})\approx0.6947\).
Then \(x = 4.1\times\cos(46^{\circ})\).
\(x=4.1\times0.6947\).
\(x\approx2.85\).

Answer:

\(x\approx2.9\)