{Geometry} Find length of the equilateral triangle

[youngstudent16]

Homework Statement

http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers [/B]

Homework Equations

The radius of the circle and properties of the equilateral triangle

The Attempt at a Solution

ThetaBig = ThetaSmall = 60

SideBig * sin(60deg)+SideSmall * sin(60deg) = 2 * radius

SideSmall = (2 * radius - SideBig * sin(60deg)) / sin(60deg)

SideSmall = 2 * radius / sin(60deg) - SideBig

This gave me fraction answer of 64/3 - 16 not in the correct form

 

[DEvens]

SideBig * sin(60deg)+SideSmall * sin(60deg) = 2 * radius

According to the picture this is not the case. The left side is actually a little bit less than 2 * radius, because the smaller triangle does not touch the circle at the bottom middle.

 

[youngstudent16]

According to the picture this is not the case. The left side is actually a little bit less than 2 * radius, because the smaller triangle does not touch the circle at the bottom middle.

Picture is human error on my part with bad paint skills

 

[DEvens]

Picture is human error on my part with bad paint skills

I don't think I made myself clear. You have worked out the combined height of the two triangles, and this is slightly less than the diameter of the circle.

 

[SteamKing]

Since we are dealing with equilateral triangles, it's not clear what "Side Big" and "Side Small" are.

 

[DEvens]

Since we are dealing with equilateral triangles, it's not clear what "Side Big" and "Side Small" are.

Look at the picture. There is a big triangle and a small triangle.

 

[youngstudent16]

Since we are dealing with equilateral triangles, it's not clear what "Side Big" and "Side Small" are.

Side big is meant to be the side of the bigger triangle which is known as 16. The small side is the one I'm trying to find expressed as Asqrt(B)-C where they are all integers.

 

[youngstudent16]

I don't think I made myself clear. You have worked out the combined height of the two triangles, and this is slightly less than the diameter of the circle.

Ah yes I ended up using law of cosines and got the correct answer thank you for the hint.