solve for ( x ). round to the nearest tenth of a degree, if necessary.
solve for ( x ). round to the nearest tenth of a degree, if necessary.
Answer
Explanation:
Step1: Identify the trigonometric ratio
In a right - triangle, we use the sine function. The formula for sine is (\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}). Here, the side opposite to angle (x) is not needed. We can also use the cosine function. But more straightforwardly, using the definition of (\sin) in the context of right - triangle (if we consider the right - triangle ( \triangle PQO) with right - angle at (P)), (\sin(x)=\frac{PO}{QO}) (incorrect approach). A better approach is using the cosine function: (\cos(x)=\frac{PQ}{QO}) (where (PQ = 73) and (QO=97)).
Step2: Calculate the angle
We know that (x=\cos^{- 1}(\frac{73}{97})). First, calculate (\frac{73}{97}\approx0.7526). Then, (x = \cos^{-1}(0.7526)). Using a calculator, (x\approx41.1^{\circ})
Answer:
(x\approx41.1^{\circ})