Calculation of length inside a circle

[thomas49th]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

But now where. What can i use to find the red line?

Thanks

 

[rock.freak667]

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

 

[thomas49th]

yep. is it possible to find the red line?

 

[symbolipoint]

You have half of an equilateral triangle.

 

[rock.freak667]

yep. is it possible to find the red line?

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

 

[thomas49th]

this is for a project not a homework question so I am 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 :)

 

[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

 

[symbolipoint]

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

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.