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Problem solving: Triangle

Red Tuxer was kind enough to post a very interesting problem with triangles. I liked it so much that I’m translating it, so everyone can enjoy solving it. Here it goes…

[ABCD] is a square. [BCE] is a equilateral triangle. What you have to find out is the amplitude of the EÂD angle.
Problem solving - Triangle
Pre-requisites: basic algebra and geometry.

Post your answers and explanations.

Última actualização: 08/06/2012

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5 comentários a Problem solving: Triangle

  1. Sergio Janeiro 19, 2007 at 16:17 #

    75…

    You just need to start with the ABC angle (90) of
    the square and estimate the ABE angle.
    Then, as both distances AB and BE are
    equal, you have the answer.

    Nice challenge !

  2. Sergio Janeiro 19, 2007 at 16:19 #

    I did not want to spoil the answer…75 is the angle
    EAB…

  3. Pedro Pais Janeiro 19, 2007 at 16:22 #

    Sergio has given quite a great clue guys. Why don’t you follow up?

  4. João Craveiro Janeiro 19, 2007 at 17:23 #

    EBC = 60º (180/30)
    EBA = 30º (90 – EBC)

    [AB] = [BE] => BÂE = BÊA = (180-EBA)÷2 = 75

    EÂD = 90-EAB = 15

    Answer: EÂD = 15º

  5. Pedro Pais Janeiro 23, 2007 at 0:23 #

    Right on João! 🙂

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