Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle CDE, we know the hypotenuse \(CE = 9.4\) and we want to find the adjacent side \(x\) to the angle \(\angle C=65^{\circ}\). We use the cosine function since \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos C=\frac{CD}{CE}\).

Step2: Substitute the values

Substitute \(C = 65^{\circ}\) and \(CE = 9.4\) into the cosine formula: \(\cos(65^{\circ})=\frac{x}{9.4}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x = 9.4\times\cos(65^{\circ})\). Since \(\cos(65^{\circ})\approx0.4226\), then \(x = 9.4\times0.4226\).

Step4: Calculate the value of \(x\)

\(x=9.4\times0.4226 = 3.97244\).

Step5: Round the answer

Rounding \(3.97244\) to the nearest tenth gives \(x\approx4.0\).

Answer:

\(4.0\)