Question

find the measure of angle x. round to the nearest tenth of a degree.

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Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\). Let the angle opposite side \(20\) be \(44^{\circ}\), and the side opposite angle \(x\) be \(20\), and the side opposite the third - angle be \(40\).
\(\frac{\sin x}{20}=\frac{\sin44^{\circ}}{40}\)

Step2: Solve for \(\sin x\)

Cross - multiply: \(\sin x=\frac{20\sin44^{\circ}}{40}\)
Since \(\sin44^{\circ}\approx0.6947\), then \(\sin x=\frac{20\times0.6947}{40}\)
\(\sin x = 0.34735\)

Step3: Find the angle \(x\)

Take the inverse sine: \(x=\sin^{- 1}(0.34735)\)
\(x\approx20.4^{\circ}\)

Answer:

\(20.4\)