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[Community Question] Geometry: Projection of tilted triangle onto a wall

One of our user asked:

A 3,4,5 triangle resting on its side of length 3 is tilted so that it makes a 60 degree angle with the floor and rests on the wall. What are the dimensions of the projection of the triangle onto the wall. The height is $2\sqrt{3}$ I can't seem to figure out how to find the length of the base. The answer given is $\frac{3}{4}2\sqrt{3}$. I'd appreciate any explanations in deriving this. Thank you.


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