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 function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, for angle \(x\), the opposite side to \(x\) is \(BC = 5.1\) and the hypotenuse is \(BD=6.8\). So, \(\sin x=\frac{BC}{BD}\).

Step2: Substitute the values

Substitute \(BC = 5.1\) and \(BD = 6.8\) into the sine formula: \(\sin x=\frac{5.1}{6.8}\). Calculate \(\frac{5.1}{6.8}=0.75\). So, \(\sin x = 0.75\).

Step3: Solve for \(x\)

To find \(x\), use the inverse - sine function \(x=\sin^{- 1}(0.75)\). Using a calculator, \(x=\sin^{-1}(0.75)\approx48.6^{\circ}\).

Answer:

\(48.6^{\circ}\)