Question

solve for $x$. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
$x =$

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 41^{\circ}\), the adjacent side to the angle \(41^{\circ}\) is \(x\), and the hypotenuse \(NP = 83\). 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:

\(62.6\)