# Homework Help: Calculation of length inside a circle

1. Nov 2, 2008

### thomas49th

1. The problem statement, all variables and given/known data

I want to find the length in red
radius is 10, angle is 30°
Is it possible?

2. Relevant equations
30° = pi/6
I can find the arc using arc length = r theta
= 10 * pi/6
= 5/3pi

3. The attempt at a solution
But now where. What can i use to find the red line?

Thanks

Last edited: Nov 2, 2008
2. Nov 2, 2008

### rock.freak667

Is the red line perpendicular to that horizontal line that makes 30 degrees?

3. Nov 2, 2008

### thomas49th

yep. is it possible to find the red line?

4. Nov 2, 2008

### symbolipoint

You have half of an equilateral triangle.

5. Nov 2, 2008

### rock.freak667

If it is perpendicular, then just consider what cos30 is and what sin30 is.

6. Nov 2, 2008

### thomas49th

this is for a project not a homework question so im not really bothered about being walked through. can you give it to me in all one go please? I know you walk people through homeworks, but I need this quite quickly :)

half an equilateral triangle because of a circle rule?
what next?
so can you DEFINAtLY calculate the the red line?

Thank you :)

7. Nov 2, 2008

### thomas49th

Wow, it's so simple, I was looking for much more complicated stuff. I know the hypotenuse and the angle therefore i can calculate the length of the opposite side using trig

8. Nov 2, 2008

### symbolipoint

The situation is simpler than that. You do not need any Trigonometry. My hint was, "you have half of an equilateral triangle." Half of an equilateral triangle is a 30-60-90 triangle; put the two halves together and you have the whole equilateral triangle. Your red segment is half of a side of the equilateral triangle. Each side of the equilateral triangle formable from your diagram is 10 units. Your red segment by itself in your diagram is 5 units.