Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle PON\), we know the hypotenuse \(PN = 9\) and the side opposite to angle \(x\) is \(PO=7.5\). We use the sine ratio. The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin x=\frac{PO}{PN}\).

Step2: Substitute the values

Substitute \(PO = 7.5\) and \(PN=9\) into the sine formula. We get \(\sin x=\frac{7.5}{9}\).

Step3: Simplify the fraction

\(\frac{7.5}{9}=\frac{75}{90}=\frac{5}{6}\approx0.8333\).

Step4: Find the angle \(x\)

To find \(x\), we use the inverse sine function. \(x = \sin^{-1}(0.8333)\). Using a calculator, \(x\approx56.4^{\circ}\).

Answer:

\(56.4\)