from the first picture ...
diagonal length =
after tilting at an angle ...
height =
height =
height =
height =
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).
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)