Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.

Correct result:

ha =  32.9
hb =  29.4
hc =  74.8

Solution:

 s=a+b+c2=96 S=s(sa)(sb)(sc)=1234.54  ha=2Sa=21234.5475=32.9 \ \\ s = \dfrac{a+b+c}{2} = 96 \ \\ S = \sqrt{ s (s-a)(s-b)(s-c)} = 1234.54 \ \\ \ \\ h _a = \dfrac{ 2S}{a} = \dfrac{ 2 \cdot 1234.54}{ 75} = 32.9
hb=2Sb=21234.5484=29.4h_b = \dfrac{ 2S}{b} = \dfrac{ 2 \cdot 1234.54}{ 84} = 29.4
hc=2Sc=21234.5433=74.8h_c = \dfrac{ 2S}{c} = \dfrac{ 2 \cdot 1234.54}{ 33} = 74.8



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