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March 20th, 2011, 03:46 PM  #1 
Newbie Joined: Mar 2011 Posts: 12 Thanks: 0  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) 
March 20th, 2011, 04:03 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: A confusing proof
We can use a rotation of axes, where the positive xaxis is rotated by b: 
March 20th, 2011, 04:05 PM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
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).

March 20th, 2011, 04:21 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: A confusing proof
Another way: Let Y be the height of P after the tilt. The diagonal of the rectangle is thus: Use additiveangle identity for sine: Using and we have: Multiply through by : 
March 20th, 2011, 04:29 PM  #5 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Cool! 
March 20th, 2011, 05:21 PM  #6 
Newbie Joined: Mar 2011 Posts: 12 Thanks: 0  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? 
March 20th, 2011, 05:24 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: A confusing proof
Yes, looks good to me. 
March 20th, 2011, 05:29 PM  #8 
Newbie Joined: Mar 2011 Posts: 12 Thanks: 0  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?

March 20th, 2011, 05:33 PM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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.

March 20th, 2011, 05:36 PM  #10 
Newbie Joined: Mar 2011 Posts: 12 Thanks: 0  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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