Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), the adjacent side to \(\theta\) is \(35\), and the hypotenuse is \(x\).
So, \(\cos(40^{\circ})=\frac{35}{x}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\cos(40^{\circ})=\frac{35}{x}\) to get \(x=\frac{35}{\cos(40^{\circ})}\).
We know that \(\cos(40^{\circ})\approx0.7660\).
Then \(x=\frac{35}{0.7660}\approx45.7\).

Answer:

\(x\approx45.7\)