Question

100 POINTS!!! ASAP-- Pls show work too TY

Answer 1

I will help you but is there any picture that can help me answer the question?

Answer 2

`\sin(\theta)=(√(13))/(7)\approx0.5151`

Explanation:

So we know that Θ is acute and that:

`\cos(\theta)=6/7`

First, note that since Θ is acute, it is between 0 and 90 degrees, meaning that all of our trig ratios will be positive since the angle is in the Quadrant I.

The Pythagorean Identity is:

`\sin^2(\theta)+\cos^2(\theta)=1`

We know that cosine is 6/7. Substitute:

`\sin^2(\theta)+((6)/(7))^2=1`

Square:

`\sin^2(\theta)+(36)/(49)=1`

Subtract both sides by 36/49. Change the 1 to 49/49 to make a common denominator:

`\sin^2(\theta)=(49)/(49)-(36)/(49)`

Subtract:

`\sin^2(\theta)=(13)/(49)`

Take the square root of both sides:

`\sin(\theta)=\pm\sqrt{(13)/(49)}`

Simplify:

`\sin(\theta)=\pm(√(13))/(7)`

As mentioned previously, since Θ is acute, all of the trig functions must be positive. So, we can ignore our negative answer:

`\sin(\theta)=(√(13))/(7)\approx0.5151`

and we're done!