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Thread: triangle

  1. #1
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    triangle

    https://www.examinations.ie/schools/...gher_Level.pdf

    I am stuck on question Q8aii ive been told that the angle is greatest vale a can have is when it makes a right angled (triangle ACF)
    i wondering why this is .
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  2. #2
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    Re: triangle

    Calculate the limit of $\alpha$ as $|DE| \to 0$.
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  3. #3
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    Re: triangle

    One rather obvious point should be that the support attached to the back only works when the panel is tilted toward the back! If \alpha> 90 degrees the panel will fall over forwards.
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  4. #4
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    Re: triangle

    I did not read the problem carefully enough. I apologize. Consider this: Draw a line segment perpendicular to AF that intersects point C. This represents the height of the triangle. Let's call the height of the triangle $h$. We know that $\sin \alpha = \dfrac{h}{25}$. So, the bigger $h$ is, the greater $\alpha$ is. Remember that if $h>22$, then the leg $CF$ would no longer touch the ground, so the maximum height is 22cm. Now, let's define $\angle CFA = \beta$. We know that $\sin \beta = \dfrac{h}{22}$. So, $h = 22\sin \beta$. The maximum value for $h$ is reached when $\beta = 90^\circ$ since that is when $h=|CF|=22$.
    Last edited by SlipEternal; May 24th 2017 at 04:12 PM.
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  5. #5
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    Re: triangle

    Quote Originally Posted by SlipEternal View Post
    I did not read the problem carefully enough.
    Oh ya? Go stand in the corner....22 minutes....
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  6. #6
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    Re: triangle

    Quote Originally Posted by DenisB View Post
    Oh ya? Go stand in the corner....22 minutes....
    Most corners are 5400 minutes = 90 degrees. A corner that is 22 minutes? That would be really narrow... Where's my protractor?
    Last edited by SlipEternal; May 24th 2017 at 05:33 PM.
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  7. #7
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    Re: triangle

    I'm still kinda confused
    I do not see why angle AFC can not be slightly greater than 90 degrees and it would still not fall over. Like say 91 degrees
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  8. #8
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    Re: triangle

    If that angle is big then $\alpha$ is small. The question is not about the biggest angle you can get in the triangle. It is about the biggest you can make $\alpha $
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