document.write( "Question 252828: What is the volume of a hexagonal pyramid when the base's side length is 3 and the angle from a point B at a vertex on the base, to point C at the radius, to point A at the top of the pyramid, is 35 degrees? Thank you SO much for your help. \n" ); document.write( "

Algebra.Com's Answer #185022 by drk(1908) $\"\"$ $\"About$

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The first thing you notice is that we have a hexagonal based pyramid.
\n" ); document.write( "--
\n" ); document.write( "step 1: find the area of the hexagon with side = 3.
\n" ); document.write( "These are pretty easy to find. Draw a segment from the center (C) to the vertex (B) and its adjacent vertex. This should make a triangle. Now each interior angle of a hexagon is 120 degrees, so our triangle is a
\n" ); document.write( "60-60-60. We use the formula for equilateral triangles,
\n" ); document.write( "(i) $\"A+=+s%5E2sqrt%283%29%2F4\"$
\n" ); document.write( "where s = 3 to get
\n" ); document.write( "(ii) $\"A+=+3%5E2sqrt%283%29%2F4\"$ = 9sqrt(3)/4.
\n" ); document.write( "This is just 1 of the six triangles in the base, so we multiply (ii) by 6 to get
\n" ); document.write( "(iii) 54sqrt(3)/4 or reduced 27sqrt(3)/2.
\n" ); document.write( "--
\n" ); document.write( "step 2 find the height of the pyramid. We know a right triangle with one angle = 35 degrees. If we drew the picture, BC = 3, angle B = 35, angle BCA = 90.
\n" ); document.write( "We can use
\n" ); document.write( "tan(35) = H/3 to get the height.
\n" ); document.write( "H ~ 3*.70021 ~ 2.10063 ~ 2.1
\n" ); document.write( "--
\n" ); document.write( "step 3: Now we can find the volume of the pyramid using step 1 and 2 answers:
\n" ); document.write( " $\"V+=+%281%2F3%29%2AB%2Ah\"$
\n" ); document.write( " $\"V+=+%281%2F3%29%2A27sqrt%283%29%2F2%2A%282.1%29\"$
\n" ); document.write( " $\"V+=+18.9%2Asqrt%283%29%2F2\"$
\n" ); document.write( "V ~ 16.37. \n" ); document.write( "

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