Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(LMN\) with right - angle at \(M\), we know the adjacent side to the angle \(N(65^{\circ})\) is \(MN = 4\) and the hypotenuse is \(LN=x\). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(65^{\circ})=\frac{4}{x}\).

Step2: Solve for \(x\)

Rearrange the equation \(\cos(65^{\circ})=\frac{4}{x}\) to get \(x=\frac{4}{\cos(65^{\circ})}\).
We know that \(\cos(65^{\circ})\approx0.4226\). Then \(x = \frac{4}{0.4226}\approx9.5\).

Answer:

\(x\approx9.5\)