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Equilateral Triangle (Posted on 2003-12-18) Difficulty: 3 of 5
Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.
Then find the length of the side of the equilateral triangle.

No Solution Yet Submitted by Ravi Raja    
Rating: 4.0000 (5 votes)

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Solution Solution | Comment 11 of 19 |
Relating the three diferent triangles using the law of cosines and the characteristic of an equilateral triangle, we obtain the transcient equation: 120=Theta+ArcCos((41-L²)/40)-ArcCos((16+L²)/(10*L)) where L=2/(Cos(60-Theta)-Cos(Theta)). Solving this transcient equation we obtain Theta=47.192123734 Degrees hence L=6.76643256751cms
  Posted by Antonio on 2003-12-20 02:38:26
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