Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(BCD\), we know the opposite side (\(BC = 5.1\)) and the hypotenuse (\(BD=6.8\)). We use the sine ratio. The sine of an angle \(x\) in a right - triangle is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin x=\frac{BC}{BD}\).

Step2: Substitute the values

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

Step3: Solve for \(x\)

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

Answer:

\(x\approx48.6^{\circ}\)