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March 20th, 2011, 03:46 PM   #1
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A confusing proof

Digram attached.

The aim is to show that the height of, P, above the floor after being tilted is h(cosb+2sinb)
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March 20th, 2011, 04:03 PM   #2
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Re: A confusing proof

We can use a rotation of axes, where the positive x-axis is rotated by -b:

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March 20th, 2011, 04:05 PM   #3
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The diagram after being tilted, draw a line perpendicular to the floor that crosses bottom right corner of the rectangle. Draw a line that is parallel to the floor that crosses bottom right corner of the rectangle. Finally draw a line perpendicular to the floor that crosses top right corner of the rectangle. We can find the height (h_1) from the floor to the bottom right corner of the rectangle by using sin b = h_1 / 2h, this will give us h_1 = 2h sin b. We can find the height h_2 = the height from floor to the top right corner of the rectangle - h_1. cos b = h_2 / h, this will give us h_2 = h cos b. Therefore the height from floor to the top right corner of the rectangle = h_2 + h_1 = h cos b + 2h sin b = h(cos b + 2 sin b).
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March 20th, 2011, 04:21 PM   #4
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Re: A confusing proof

Another way:

Let Y be the height of P after the tilt. The diagonal of the rectangle is thus:



Use additive-angle identity for sine:



Using and we have:



Multiply through by :

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March 20th, 2011, 04:29 PM   #5
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Cool!
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March 20th, 2011, 05:21 PM   #6
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Re: A confusing proof

I solved it but it was just a different way of marks

In the rectangle you can work out
Length OP=h?5
sina=1/?5
cosa=2/?5

height=h?5.sin(a+b)
=h?5.(sinacosb+cosasinb)
=h?5.(1/?5cosb+2/?5sinb)
=h(cosb+2sinb)

does this working look right?
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March 20th, 2011, 05:24 PM   #7
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Re: A confusing proof

Yes, looks good to me.
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March 20th, 2011, 05:29 PM   #8
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Re: A confusing proof

ok good, im doing revision for an exam and this is the sort of question they will ask. If i was to use the same working as this would it be correct? or would you recommend a different way?
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March 20th, 2011, 05:33 PM   #9
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Re: A confusing proof

I can't see any problems with what you did...I can't speak for your professor, but every step you used is valid.
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March 20th, 2011, 05:36 PM   #10
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Re: A confusing proof

Thanks, i just needed to check I havnt made any small errors. Thanks for all your help today
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