Question

question 5 of 25
\\( \sin \theta = \frac { 8 } { 17 } \\). find \\( \tan \theta \\).
\\( \bigcirc \\) a. \\( \frac { 17 } { 15 } \\)
\\( \bigcirc \\) b. \\( \frac { 15 } { 8 } \\)
\\( \bigcirc \\) c. \\( \frac { 16 } { 17 } \\)
\\( \bigcirc \\) d. \\( \frac { 8 } { 15 } \\)

Explanation:

Step1: Recall sine definition

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{17}$, so opposite = 8, hypotenuse = 17.

Step2: Calculate adjacent side

Use Pythagorean theorem: $\text{adjacent} = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225} = 15$.

Step3: Find tanθ

$\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{15}$.

Answer:

B. $\frac{8}{15}$