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Measure that angle V (Posted on 2005-10-24) Difficulty: 4 of 5
A certain triangle ABC has D on AB and E on AC such that AD=DB=BC=CE and AE=ED. What is the measure of angle BAC?

See The Solution Submitted by Brian Smith    
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Solution re: solution -- closed form | Comment 4 of 7 |
(In reply to solution by Charlie)

Going to http://www.1728.com/cubic2.htm to see how to solve cubic equations, I found the value for x (one side of the small isosceles triangle ADE), to be

((37+9*sqrt(17))^(1/3) + (37-9*sqrt(17))^(1/3) - 2) / 3

The angle is still arccos(1/(2*x)) or

arcsec(2*((37+9*sqrt(17))^(1/3) + (37-9*sqrt(17))^(1/3) - 2) / 3)


  Posted by Charlie on 2005-10-24 15:18:40
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