Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle CDE, we know the hypotenuse \(CE = 6.6\) and we want to find the adjacent side \(x\) to the angle \(\angle E=73^{\circ}\). We use the cosine function since \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
\(\cos E=\frac{x}{CE}\)

Step2: Substitute values

Substitute \(E = 73^{\circ}\) and \(CE = 6.6\) into the formula.
\(\cos(73^{\circ})=\frac{x}{6.6}\)

Step3: Solve for \(x\)

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

Step4: Round to the nearest tenth

Rounding \(1.9272\) to the nearest tenth gives \(1.9\)

Answer:

\(1.9\)