Question

find sin(\beta) in the triangle. choose 1 answer: \\( \boldsymbol{\frac{15}{17}} \\) \\( \boldsymbol{\frac{8}{17}} \\) \\( \boldsymbol{\frac{15}{8}} \\) \\( \boldsymbol{\frac{8}{15}} \\) (triangle with right angle at c, bc=8, ac=15, ab=17, angle \\( \beta \\) at b)

Explanation:

Step1: Recall sine definition

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

Step2: Identify sides for $\beta$

For angle $\beta$, opposite side is $AC = 15$, hypotenuse is $AB = 17$.

Step3: Calculate $\sin(\beta)$

$\sin(\beta) = \frac{15}{17}$.

Answer:

A. $\dfrac{15}{17}$