Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle DEF, we know the adjacent side to the angle \(19^{\circ}\) is \(DE = 0.6\) and we want to find the hypotenuse \(x\). We use the cosine function since \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos(19^{\circ})=\frac{0.6}{x}\).

Step2: Solve for \(x\)

Cross - multiply to get \(x\cos(19^{\circ}) = 0.6\), then \(x=\frac{0.6}{\cos(19^{\circ})}\).
We know that \(\cos(19^{\circ})\approx0.9455\). So \(x=\frac{0.6}{0.9455}\approx0.6\).

Answer:

\(0.6\)