Hi! I have another geometry problem that I'm stuck on, can someone give me a hint or push me in the right direction?

The vertices of triangle ABC lie on the sides of equilateral triangle DEF, as shown. If CD = 3, CE = BD = 2, and angle ACB = 90, then find AE.

Here's the diagram:

Thank you in advance!

ConfuzzledKitten Jun 23, 2020

#1**+4 **

1) Find BC (use the Law of Cosines)

2) Find angle(DCB) (use either Law of Sines or Law of Cosines)

3) Find angle(ACE)

4) Find angle(CAE)

5) Find AE.

geno3141 Jun 23, 2020

#4**+1 **

I tried what you said up until the last step, I'm probably missing ONE tiny bit but I can't seem to figure out how to do it...

ConfuzzledKitten
Jun 26, 2020

#5**+3 **

I didn't quite get what geno said, and I tried something different. I basically used law of cosines to find all 3 side lengths of ABC in terms of AE, then solved for it with pythagoras. It worked!

ConfuzzledKitten Jun 26, 2020