Results 1 to 5 of 5

Math Help - How much is alpha ?

  1. #1
    Newbie
    Joined
    Jul 2010
    From
    Maa'le edomim-near Jerusalem
    Posts
    24

    How much is alpha ?

    Can you help me to solve this problem ?

    The answer must be just by geometric prove .Not by trigonometric !!!
    Attached Thumbnails Attached Thumbnails How much is alpha ?-1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    From the figure, we know that \angle ABC = \angle ACB = 50^o

    So, \angle DCB = 30^o

    From triangle ACD, we know that \angle ADC = 150^o

    So, we get some equations now.

    Let's give some names to the other angles:

    \angle ABD = a

    \angle DBC = b

    \angle BDC = c

    From triangle ABD, we know that: 70^o + \alpha + a = 180^o

    From triangle DBC, we know that: b + c + 30^o = 180^o

    And lastly, we know that \alpha + 150^o + c = 360^o

    and b + c = 50^o

    There is enough information to find alpha
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Unknown008 View Post
    From the figure, we know that \angle ABC = \angle ACB = 50^o

    So, \angle DCB = 30^o

    From triangle ACD, we know that \angle ADC = 150^o

    So, we get some equations now.

    Let's give some names to the other angles:

    \angle ABD = a

    \angle DBC = b

    \angle BDC = c

    From triangle ABD, we know that: 70^o + \alpha + a = 180^o

    From triangle DBC, we know that: b + c + 30^o = 180^o

    And lastly, we know that \alpha + 150^o + c = 360^o

    and b + c = 50^o That should be a + b = 50.

    There is enough information to find alpha
    Unfortunately, that is not enough information to find alpha. There are four equations for four unknowns, but they are not independent. (The fourth equation, in its corrected form above, is just what you get by adding the first two equations and subtracting the third.)

    By trigonometry I get the answer to be that \alpha = 70^\circ, but I cannot see any way of proving that by synthetic geometry. This seems to be a variant of the notorious 80-80-20 triangle problem, but maybe this one is even harder.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    You're right... that's what happens when I had a diagram with alpha, beta, gamma, delta, etc and making a post with other letters...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,113
    Thanks
    68
    Quote Originally Posted by Opalg View Post
    Unfortunately, that is not enough information to find alpha.
    You mean "fortunately", right
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Let alpha be a real number, alpha > -1 now show that
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: November 27th 2011, 08:14 PM
  2. Replies: 1
    Last Post: November 14th 2011, 03:48 AM
  3. How much is alpha?
    Posted in the Geometry Forum
    Replies: 4
    Last Post: June 19th 2011, 05:08 AM
  4. [SOLVED] \tan{2\alpha}=24/7
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 12th 2011, 02:06 PM
  5. derive cos(alpha+beta) sin(alpha+beta)?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 7th 2008, 04:27 PM

Search Tags


/mathhelpforum @mathhelpforum