php - Percentage size of the rectangle over the inner rectangle -

php - Percentage size of the rectangle over the inner rectangle -

i need know how much need zoom inner box rotate outer rectangle 12 degrees , touched inner rectangle 4 sides on perimeter.

for example, have image 400x300px.

in image in photoshop, rotated inner rectangle 12 degrees , zoom width on 113%, , height on 126% (how see eye).

i'm not math major , don't know if there's improve way of solving this, here's how go it.

let's take @ figure:

you know fact of triangles right triangles every ∠z beingness equal 90 degrees. know fact every ∠x equal 12 degrees because that's angle of rotation. therefore, 180 - (90 + 12) leaves every ∠y beingness equal 78 degrees. therefore, of angles calculated. know sides of original rectangle are, therefore, know hypotenuse of each of triangles is. makes easy solve remaining sides using formula:

sin∠n = opposite/hypotenuse

as example, let's we're solving left side of top triangle. let's phone call f. here's how look:

sin∠12 = f/a 0.208 = f/a a(0.208) = f ... , on...

12, in case ∠x. side opposite of f, looking for.

you need solve 1 pair of adjacent triangles, since other mirror results. 1 time know length of top side of top triangle, example, , length top side of right triangle, can combine 2 total length. perform similar calculation either left or right side. if know values of outer triangle, instead of inner, default, perform calculations based on defaults. 1 time know other triangle's dimensions, can calculate difference.

i don't know if illustration efficient way of doing this, it's easy me understand. hope helps.

php math geometry