document.write( "Question 621181: Find the altitudes of a triangle whose side lengths are 13, 14, and 15 \n" ); document.write( "
Algebra.Com's Answer #390627 by tomlaidlaw(14)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: SSS Triangle Solver 3 sides
Use Heron's Formula for Area:
\n" ); document.write( " First calculate s=(a+b+c)/2, then:
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\n" ); document.write( " Use the Law of Cosines for the angles:
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\n" ); document.write( " side a = 13
\n" ); document.write( " side b = 14
\n" ); document.write( " side c = 15
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\n" ); document.write( " AngleA = 53.130 degrees or 0.927 radians
\n" ); document.write( " AngleB = 59.490 degrees or 1.038 radians
\n" ); document.write( " AngleC = 67.380 degrees or 1.176 radians
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\n" ); document.write( " Area K = 84.000
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\n" ); document.write( " Circumcircle Radius = 8.125 __(R = .5a/sinA)
\n" ); document.write( " incircle radius = 4.000 __(r = 2K/(a+b+c))
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\n" ); document.write( " height over side a = 12.923 __(ha = csinB)
\n" ); document.write( " height over side b = 12.000 __(hb = asinC)
\n" ); document.write( " height over side c = 11.200 __(hc = bsinA)
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\n" ); document.write( " Thanks to hummingbird for the use of his solver. Thanks to Wolfram Math World for the triangle graphic.
\n" ); document.write( " Tom Laidlaw
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