Homework Help: {Geometry} Find length of the equilateral triangle

1. Jul 23, 2015

youngstudent16

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

2. Relevant equations
The radius of the circle and properties of the equilateral triangle

3. 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

2. Jul 23, 2015

DEvens

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.

3. Jul 23, 2015

youngstudent16

Picture is human error on my part with bad paint skills

4. Jul 23, 2015

DEvens

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.

5. Jul 23, 2015

SteamKing

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

6. Jul 23, 2015

DEvens

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

7. Jul 23, 2015

youngstudent16

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.

8. Jul 23, 2015

youngstudent16

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