Question

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

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 64^{\circ}\), the adjacent side to the \(64^{\circ}\) angle is \(2.8\), and the hypotenuse is \(x\). So, \(\cos64^{\circ}=\frac{2.8}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{2.8}{\cos64^{\circ}}\). Since \(\cos64^{\circ}\approx0.4384\), then \(x = \frac{2.8}{0.4384}\).

$$x=\frac{2.8}{0.4384}\approx6.4$$

Answer:

\(x\approx6.4\)