A board leaning against a fence makes an angle of 30 degrees with the horizontal, If the board is 4 feet long, what is the diameter of the largest pipe which will fit between the board, the fence, and the ground?

Question

anonymous · Answer

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lyrae · Answer

The circle representing the pipe is called inscribed circle or incircle.

The fomula for finding the radius of an incricle is actually quite simple:
r = 2A / P

multiplying by two we get:
D = 4A / P

where A is the area and P is the perimeter of the triangle.

radar · Answer

Area (A) can be solved by the equation for Area, A=(1/2) b(base) X h (height)
A=(1/2)bh.  You can calculate base using the cosine 30 function, height can be solved using sine 30 function.  

You can then solve P (perimeter) by adding the base plus the height plus the hypotenuse which is given as 4.

After that use the equation provided by Lyrae.

anonymous · Answer

Yeah it would be easier if I could use a Solid Mensuration solution but we are required to do it in Analytical Geometric way...but thanks anyway ^^