Question

question
solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2

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, \(\sin x=\frac{5.1}{6.8}\).

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

\(\frac{5.1}{6.8}=0.75\). So, \(\sin x = 0.75\).

Step3: Find the value of \(x\)

We know that if \(\sin x=a\), then \(x=\sin^{- 1}(a)\). So, \(x=\sin^{-1}(0.75)\). Using a calculator, \(x\approx48.6^{\circ}\).

Answer:

\(48.6^{\circ}\)