Triangle ABC

Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.

Result

hAB =  15.09

Solution:

a2=c2c c2=18233=9.82 c1=c−c2=33−9.82=23.18 hAB=c1c2=(33−18233)⋅18233=15.09a^2 = c_2 c \ \\ c_2 = \dfrac{ 18^2 }{ 33 } = 9.82 \ \\ c_1 = c - c_2 = 33 - 9.82 = 23.18 \ \\ h_{AB} = \sqrt{c_1 c_2} = \sqrt{(33 - \dfrac{ 18^2}{ 33}) \cdot \dfrac{ 18^2}{ 33}} = 15.09

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