Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle CDE\) (assuming it's a right - triangle with right - angle at \(D\)), we know the hypotenuse \(CE = 6.6\) and we want to find the adjacent side \(x\) to the angle \(L = 73^{\circ}\). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(73^{\circ})=\frac{x}{6.6}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(73^{\circ})=\frac{x}{6.6}\) by \(6.6\). We get \(x = 6.6\times\cos(73^{\circ})\).
We know that \(\cos(73^{\circ})\approx0.292\). Then \(x = 6.6\times0.292\).
\(x=6.6\times0.292 = 1.9272\)

Answer:

\(x\approx1.9\)