Question

if $c = 17$ in. and $b = 15$ in., find the value of $sin \theta$. write your answer as a fraction. you do not need to simplify
(hint: find the ratio for the bottom right angle)
(1 point)
$\frac{8}{17}$
$\frac{15}{17}$
$\frac{8}{15}$
$\frac{17}{15}$

Explanation:

Step1: Calculate side length $a$

Use Pythagorean theorem: $a = \sqrt{c^2 - b^2} = \sqrt{17^2 - 15^2} = \sqrt{289 - 225} = \sqrt{64} = 8$

Step2: Define $\sin\theta$ ratio

$\sin\theta = \frac{\text{opposite side to } \theta}{\text{hypotenuse}} = \frac{a}{c}$

Step3: Substitute values

$\sin\theta = \frac{8}{17}$

Answer:

$\frac{8}{17}$ (Option: $\frac{8}{17}$)