Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle NOP\) with right - angle at \(O\), we know the hypotenuse \(NP = 83\) and we want to find the adjacent side \(x\) (side \(OP\)) to the angle \(41^{\circ}\). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(41^{\circ})=\frac{x}{83}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(41^{\circ})=\frac{x}{83}\) by \(83\). We get \(x = 83\times\cos(41^{\circ})\).
Using a calculator, \(\cos(41^{\circ})\approx0.7547\). Then \(x = 83\times0.7547\).
\(x=83\times0.7547 = 62.6401\approx62.6\)

Answer:

\(62.6\)