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, \(\theta = 36^{\circ}\), the adjacent side is \(x\), and the hypotenuse is \(2.6\). So, \(\cos(36^{\circ})=\frac{x}{2.6}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(36^{\circ})=\frac{x}{2.6}\) by \(2.6\). We get \(x = 2.6\times\cos(36^{\circ})\). Using a calculator, \(\cos(36^{\circ})\approx0.8090\). Then \(x=2.6\times0.8090 = 2.1034\).

Answer:

\(x\approx2.1\)