Question

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

Explanation:

Step1: Recall the 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 \(x = 2.6\times\cos(36^{\circ})\).
Since \(\cos(36^{\circ})\approx0.809\), then \(x = 2.6\times0.809 = 2.1034\approx2.1\).

Answer:

\(x = 2.1\)