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Problem:

A 4 inch square sits in a corner(picture x,y origin). A 12 inch ruler or line leans against the wall at an angle such that there are 3 points of contact: wall, the outer corner of the block, and the floor.

At what point on the ruler does the corner of the block make contact?

Efforts:

We know that the upper triangle and lower triangle are of same angles. (Ruler passes through 2 paralell lines, being the floor and the top of the 4 inch block. So the trig function ratios are equal.

I have gone the route of setting the large triangle hypotenuse (12) equal to the sum of the hypotenuses of the smaller triangles leading me down a path that still leaves me with 2 variables.

I would appreciate some input as to a fresh way of approaching this problem, not necessarily the answer.