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  • Basic Math Puzzle: Find Dr. Gibbus' Angle

    Kaustubh Katdare

    Administrator

    Updated: Oct 25, 2024
    Views: 1.3K
    CEans,

    I found an interesting puzzle on the Internet here -

    Puzzle#110 - <a href="https://www.archimedes-lab.org/page10b.html" target="_blank" rel="noopener noreferrer">Puzzles of the Month</a>

    The puzzle is as follows -

    Find the "Professor Gibbus' Angle" below -

    [​IMG]

    Difficulty Level: (2/5) , Basic Mathematics Knowledge.

    Post your answers and the logic that you used to calculate the angle 'alpha'. All the best 😁

    -The Big K-
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  • RachaelP

    Member • Mar 18, 2007

    Well this is my first post so I hope I get this correct.

    Rach
    Here goes....

    We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.

    The angle of each of the triangles can be calculated by:

    angle = tan-1 opposite/adjacent

    So....

    For the 2x1 triangle:

    angle = tan-1 2 = 63.435

    For the 3x1 triangle:

    angle = tan-1 3 = 71.565

    Therefore....

    alpha = 180 - 63.435 - 71.565

    So the Dr. Gibbus' Angle is 45 degrees.



    ​
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  • Ellie

    Member • Mar 18, 2007

    This can also be acheived in a simpler way as follows....

    Leave computer chair and go to drawers

    Rifle through drawers and find protractor

    Go and sit back in computer chair

    Put protractor on monitor and measure angle

    Answer = 45 degrees

    Ellie 😕 😁
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  • Kaustubh Katdare

    Administrator • Mar 18, 2007

    Ellie
    This can also be acheived in a simpler way as follows....

    Leave computer chair and go to drawers

    Rifle through drawers and find protractor

    Go and sit back in computer chair

    Put protractor on monitor and measure angle

    Answer = 45 degrees

    Ellie 😕 😁

    No doubt you are a Crazy Engineer 😁 . But then, Logic is our best friend. It helps us in many situations.

    Good approach, I must say. But I was wondering if anyone of us can actually tell us the solution for this problem.

    -The Big K-
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  • djnachi

    Member • Mar 19, 2007

    Ellie
    This can also be acheived in a simpler way as follows....

    Leave computer chair and go to drawers

    Rifle through drawers and find protractor

    Go and sit back in computer chair

    Put protractor on monitor and measure angle

    Answer = 45 degrees

    Ellie 😕 😁

    Hi Ellie,

    Got to say., you got Humorously Smart Brain. 😉
    But i still wonder, is it actually the right way to find the Gibbus' Angle?? 😒

    Regards,
    Dj Nachi. 😀
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  • djnachi

    Member • Mar 19, 2007

    RachaelP
    Well this is my first post so I hope I get this correct.



    Rach
    Here goes....​

    We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.​

    The angle of each of the triangles can be calculated by:​

    angle = tan-1 opposite/adjacent​

    So....​

    For the 2x1 triangle:​

    angle = tan-1 2 = 63.435​

    For the 3x1 triangle:​

    angle = tan-1 3 = 71.565​

    Therefore....​

    alpha = 180 - 63.435 - 71.565​

    So the Dr. Gibbus' Angle is 45 degrees.​
    Hi Rachael,
    Hats Off ... 😁
    You made it so easy to understand. Me priety messy with mathematics but i still tried to apply few of my basics but eventually failed. So i really appreciate the fact that you so very well systematically got it.
    Congrats !!!

    Regards,
    Dj Nachi. 😀
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  • Rocker

    Member • Mar 19, 2007

    RachaelP
    Well this is my first post so I hope I get this correct.

    Rach
    Here goes....

    We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.

    The angle of each of the triangles can be calculated by:

    angle = tan-1 opposite/adjacent

    So....

    For the 2x1 triangle:

    angle = tan-1 2 = 63.435

    For the 3x1 triangle:

    angle = tan-1 3 = 71.565

    Therefore....

    alpha = 180 - 63.435 - 71.565

    So the Dr. Gibbus' Angle is 45 degrees.



    ​
    I agree with the solution. But I guess there is a simpler way of calculating it. I can't calculate tan -1 mentally 😁
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  • Kaustubh Katdare

    Administrator • Apr 23, 2007

    and the answer is ...

    Okay, we have had lot of fun solving the problem. Its high time that we post the solution.

    Have a look at this -

    [​IMG]

    That was simple, what say? 😁

    -The Big K-
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