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Rotating rectangle

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[quote][i]Originally posted by daimath[/i]
[br]Assume :

1. A square rectangle of given width..
2. The square rectangle is superimposed on a field (think of a square postcard lying on a sheet of graph paper).
3. The rectangle has an initial orientation of horizontal and vertical sides (i.e. it lines up with the lines of the graph paper).

At this stage, the horizontal size of the field occupied by the rectangle will be equal to the width of the rectangle.  Similarly, the vertical size of the field occupied by the rectangle will be equal to the height of the rectangle.

Now assume that from that start position the rectangle is rotated by x degrees clockwise around its center.

For increasing values of x between 0 and 45  the horizontal  width of the field occupied by the rectangle will increase.  After 45 degrees has been reached further increasing the value of x decreases the width of the field occupied by the rectangle.  When x = 90 degrees the width of the field occupied by the rectangle will again be equal to the width of the rectangle.

My question is what formula will solve the following question :

Given a known width for the rectangle and a known clockwise rotation angle between 0 and 90 degrees what is the horizontal size of the field occupied by the rectangle?  The answer can be expressed as a multiple of the width of the rectangle.
[/quote]

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T O P I C R E V I E W

daimath

Posted - 06/15/2012 : 23:04:22

Assume :

1. A square rectangle of given width..
2. The square rectangle is superimposed on a field (think of a square postcard lying on a sheet of graph paper).
3. The rectangle has an initial orientation of horizontal and vertical sides (i.e. it lines up with the lines of the graph paper).

At this stage, the horizontal size of the field occupied by the rectangle will be equal to the width of the rectangle. Similarly, the vertical size of the field occupied by the rectangle will be equal to the height of the rectangle.

Now assume that from that start position the rectangle is rotated by x degrees clockwise around its center.

For increasing values of x between 0 and 45 the horizontal width of the field occupied by the rectangle will increase. After 45 degrees has been reached further increasing the value of x decreases the width of the field occupied by the rectangle. When x = 90 degrees the width of the field occupied by the rectangle will again be equal to the width of the rectangle.

My question is what formula will solve the following question :

Given a known width for the rectangle and a known clockwise rotation angle between 0 and 90 degrees what is the horizontal size of the field occupied by the rectangle? The answer can be expressed as a multiple of the width of the rectangle.

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