Question

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

Explanation:

Step1: Use cosine function

In right - triangle \(NML\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 46^{\circ}\), the adjacent side to the angle \(46^{\circ}\) is \(x\), and the hypotenuse \(NL = 4.1\). 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 get \(x = 4.1\times\cos(46^{\circ})\). Using a calculator, \(\cos(46^{\circ})\approx0.6947\). Then \(x=4.1\times0.6947 = 2.84827\).

Answer:

\(x\approx2.8\)