SOLUTION: Find the altitudes of a triangle whose side lengths are 13, 14, and 15

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Question 621181: Find the altitudes of a triangle whose side lengths are 13, 14, and 15
Answer by tomlaidlaw(14)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: SSS Triangle Solver 3 sides
Use Heron's Formula for Area:
First calculate s=(a+b+c)/2, then:

Use the Law of Cosines for the angles:

side a = 13
side b = 14
side c = 15

AngleA = 53.130 degrees or 0.927 radians
AngleB = 59.490 degrees or 1.038 radians
AngleC = 67.380 degrees or 1.176 radians

Area K = 84.000

Circumcircle Radius = 8.125 __(R = .5a/sinA)
incircle radius = 4.000 __(r = 2K/(a+b+c))

height over side a = 12.923 __(ha = csinB)
height over side b = 12.000 __(hb = asinC)
height over side c = 11.200 __(hc = bsinA)

Thanks to hummingbird for the use of his solver. Thanks to Wolfram Math World for the triangle graphic.
Tom Laidlaw
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