Question

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

Explanation:

Step1: Use sine - function definition

In right - triangle \(MLK\) with right angle at \(L\), \(\sin x=\frac{opposite}{hypotenuse}\). Here, the side opposite to angle \(x\) is \(LK = 69\) and the hypotenuse is \(MK=92\). So, \(\sin x=\frac{69}{92}\).

Step2: Simplify the fraction

\(\frac{69}{92}=\frac{3}{4}= 0.75\). So, \(\sin x = 0.75\).

Step3: Find the inverse - sine

To find \(x\), we use the inverse - sine function, \(x=\sin^{-1}(0.75)\).

Step4: Calculate the value

Using a calculator, \(x=\sin^{-1}(0.75)\approx48.6^{\circ}\).

Answer:

\(48.6^{\circ}\)