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I am building a sloped table and I need to determine the height of one side. Here are my dimensions. The tall side has two legs at a height of $55$ inches, the top where the tabletop attaches will be cut at a $60^\circ$ angle. The Distance from where the tall legs attach to the next set of legs is $34$ inches. The next set of legs will be also cut at a $60^\circ$ angle, however I am not sure how to calculate what height the second set of legs should be. I have added a image to explain. Hopefully some one can help. enter image description here

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    @Anders: That doesn't tell me which angle you are measuring (I'm no carpenter): the one on "top left" or the one on "bottom right".2012-04-25

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Since Brett Frankel never placed his comment in this box, I'll do it: the height is $55−34\sin(60^\circ) \approx 25.5$