Question

use the diagram to answer the question.
diagram of a right triangle with top horizontal side 9, vertical leg 40, hypotenuse 41, right angle at the top, angle θ at the bottom vertex *diagram not drawn to scale
which is \\( \sin \theta \\)?
\\( \bigcirc \\) a. \\( \sin \theta = \frac{9}{41} \\)
\\( \bigcirc \\) b. \\( \sin \theta = \frac{9}{40} \\)
\\( \bigcirc \\) c. \\( \sin \theta = \frac{40}{41} \\)
\\( \bigcirc \\) d. \\( \sin \theta = \frac{41}{40} \\)
\\( \bigcirc \\) e. \\( \sin \theta = \frac{41}{9} \\)

Explanation:

Step1: Recall Sine Definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify Sides for $\theta$

For angle $\theta$, the opposite side is 9, hypotenuse is 41.

Step3: Apply Sine Formula

$\sin\theta = \frac{9}{41}$.

Answer:

A. $\sin\theta = \frac{9}{41}$