Proving the Height of Tilted P After Rotation | Triangle Method

[chris99191]

1. For the diagram in the attachment, prove that the height of P above floor after being tilted is h(cosb+2sinb)


2. h(cosb+2sinb)


3. I think you need to divide them up into triangles and then use the angles for each as well as maybe using a sums to products formula

 

[CompuChip]

Let's call the bottom right point of the rectangle A, and the top left corner B, such that we are looking at rectangle OAPB.

In the rotated version, you can draw a horizontal line through A. Then, since OAP is a right angle, you can use the Z-shape in the figure to find the two subangles.
From there on it's basic geometry to find the height of B, and the difference in height between B and P.

Hopefully it is clear from the text what I meant. If not let me know, I can upload an image.

 

[chris99191]

That sounds pretty good haha
except i don't understand where the z-shape is. Is it PA,AB and BO? and what do you mean by subangles

 

[CompuChip]

OK, here is the hint graphically.

Note the red line parallel to the horizontal line through O, and the angles marked in green.

 

[chris99191]

i feel stupid for asking this but what subangles should i now find

 

[CompuChip]

First of all, can you now find the height of the red line above the origin?