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 a right - triangle \( \triangle PQO\) with right - angle at \(P\), we know the hypotenuse \(OQ = 18\) and the side adjacent to the angle \(x\) is \(PQ=8.5\). We use the cosine ratio. The cosine of an angle in a right - triangle is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos x=\frac{PQ}{OQ}\).

Step2: Substitute the values

Substitute \(PQ = 8.5\) and \(OQ = 18\) into the cosine formula. We get \(\cos x=\frac{8.5}{18}\).

Step3: Solve for \(x\)

Take the inverse cosine (arccos) of both sides. \(x=\cos^{-1}(\frac{8.5}{18})\). Using a calculator, \(\frac{8.5}{18}\approx0.4722\). Then \(x=\cos^{-1}(0.4722)\approx61.8^{\circ}\).

Answer:

\(61.8\)