solve for $x$. round to the nearest tenth of a degree, if necessary.\nanswer attempt 1 out of 2\n$x =$
solve for $x$. round to the nearest tenth of a degree, if necessary.\nanswer attempt 1 out of 2\n$x =$
Answer
Explanation:
Step1: Identify the trigonometric ratio
In a right - triangle, the sine of an angle (x) is defined as (\sin x=\frac{\text{opposite}}{\text{hypotenuse}}). Here, the side opposite to angle (x) is (OP), and the hypotenuse is (OQ = 18), and (PQ=8.5) (adjacent side). We use the cosine ratio (\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}).
Step2: Apply the cosine formula
We know that (\cos x=\frac{PQ}{OQ}). Substituting (PQ = 8.5) and (OQ=18) into the formula, we get (\cos x=\frac{8.5}{18}).
Step3: Solve for (x)
Take the inverse cosine of both sides: (x=\cos^{-1}(\frac{8.5}{18})). [x=\cos^{-1}\left(\frac{8.5}{18}\right)\approx61.9^{\circ}]
Answer:
(61.9)