To find the angle where the ruler touches the desk, you start by considering the right triangle formed with the desk, the height of the books, and the length of the ruler. The height of the books (7 inches) serves as the opposite side, and the length of the ruler (12 inches) serves as the hypotenuse.
To solve for the angle, [tex]\(\theta\)[/tex]:
1. Identify the trigonometric function: In this case, we use the sine function because we have the lengths of the opposite side and the hypotenuse.
2. Set up the sine function:
[tex]\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{12}
\][/tex]
3. Solve for the angle [tex]\(\theta\)[/tex]:
[tex]\[
\theta = \arcsin\left(\frac{7}{12}\right)
\][/tex]
4. Convert the angle from radians to degrees: In this step, you would typically use the arcsine function and then convert the radians to degrees if you're doing it manually.
5. Round the result to the nearest hundredth.
Through these steps, the calculated angle [tex]\(\theta\)[/tex] is approximately [tex]\(35.69^\circ\)[/tex].
So, the best answer from the provided choices is:
B. [tex]\(35.69^\circ\)[/tex]
