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Math Help - A proof my friend got me to do

  1. #1
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    A proof my friend got me to do

    My friend and I both like simple calculus, he showed me this proof which looks straightforward however i could not do it. I drew a diagram on paint and it is an attachment. The aim is to show that the height of P above the floor after being tilted is h(cosb+2sinb).
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  2. #2
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    from the first picture ...

    diagonal length = \sqrt{5} \cdot h

    \sin(a) = \dfrac{1}{\sqrt{5}}

    \cos(a) = \dfrac{2}{\sqrt{5}}

    after tilting at an angle b ...

    height = \sqrt{5} \cdot h \cdot \sin(a+b)<br />

    height = \sqrt{5} \cdot h [\sin(a)\cos(b) + \cos(a)\sin(b)]<br />

    height = \sqrt{5} \cdot h \left[\dfrac{1}{\sqrt{5}} \cdot \cos(b) + \dfrac{2}{\sqrt{5}} \cdot \sin(b) \right]

    height = h \left[\cos(b) + 2\sin(b) \right]
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  3. #3
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    Can someone please check my proof

    I completed this proof in the attachment but can someone please check my working

    The aim was to show that the height of P above floor after the crate is tilted is h(cosb+2sinb)

    From the rectangles you can work out
    Length of OP=h√5
    sin(a)=1/√5
    cos(a)=2/√5

    therefore
    height=h√5.sin(a+b)
    =h√5.(sinacosb+cosasinb)
    =h√5.(1/√5cosb+2/√5sinb)
    =h(cosb+2sinb)
    Attached Thumbnails Attached Thumbnails A proof my friend got me to do-proof.jpg  
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