Question

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

Explanation:

Step1: Identify the trigonometric ratio

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

Step2: Substitute the values into the formula

Here, \(\theta = 46^{\circ}\), adjacent \(=x\), hypotenuse \(=4.1\). So, \(\cos(46^{\circ})=\frac{x}{4.1}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x = 4.1\times\cos(46^{\circ})\).
We know that \(\cos(46^{\circ})\approx0.6947\) (using a calculator). Then \(x=4.1\times0.6947\).
\(x = 2.84827\approx2.9\) (rounded to the nearest tenth).

Answer:

$x\approx2.9$