SOLUTION: Let T be a point inside square EFGH such that TE = 1, TF = 2, and TG = 3. Find < ETF. I think the first step is to make another square rotated 90 degrees with F as the origin.

Algebra ->  Points-lines-and-rays -> SOLUTION: Let T be a point inside square EFGH such that TE = 1, TF = 2, and TG = 3. Find < ETF. I think the first step is to make another square rotated 90 degrees with F as the origin.       Log On


   

Question 1153570: Let T be a point inside square EFGH such that TE = 1, TF = 2, and TG = 3. Find < ETF. I think the first step is to make another square rotated 90 degrees with F as the origin.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem is for advanced students  (Math circle level or  Math  Olympiad level).

            Therefore,  I will be very short and will give the basic idea,  only. 


The given data allow to determine the side length of the given square.



    How to do it, you will find in the lesson
  
        - Find the side of a square if distances are given from an interior point to 3 its vertices 

    in this site, where similar problem was solved.



By knowing the square side length, you may apply then the Cosine Law and to find the angle ETF.

Happy learning and happy solving (!)