Question

can someone please help mee

Answer 1

Answer:

$\frac{\sqrt{731}}{30}$

Step-by-step explanation:

We first observe that the angle is located in quadrant III

This allows us to draw a triangle as attached in the attachments.

Using this triangle, we can find sin($\theta_1$).

Remembering that sin(theta) = $\frac{opp}{hypo}$, we can see from the attached image that it is $\frac{\sqrt{30^2 - 13^2}}{30}$, then simplifying $\sqrt{30^2 - 13^2}$ using a calculator, we get $\sqrt{731}$.

So our final answer is the answer shown above.

You may be wondering how did the side lengths appear on the triangle.

From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.