Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(x\), the side opposite to \(x\) is \(BC = 3.3\) and the hypotenuse \(AC=6\). So, \(\sin x=\frac{3.3}{6}\).

Step2: Calculate the value of \(\sin x\)

\(\sin x=\frac{3.3}{6}=0.55\).

Step3: Find the angle \(x\)

To find \(x\), use the inverse - sine function \(x = \sin^{-1}(0.55)\). Using a calculator, \(x\approx33.4^{\circ}\).

Answer:

\(33.4^{\circ}\)