# RT triangle and height

Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.

Result

a =  3 cm
c =  5 cm

#### Solution:

$b=4 \ \\ h=2.4 \ \\ \ \\ b^2=c_{1}^2+h^2 \ \\ c_{1}=\sqrt{ b^2-h^2 }=\sqrt{ 4^2-2.4^2 }=\dfrac{ 16 }{ 5 }=3.2 \ \\ \ \\ c_{1}c_{2}=h^2 \ \\ c_{2}=h^2/c_{1}=2.4^2/3.2=\dfrac{ 9 }{ 5 }=1.8 \ \\ \ \\ c=c_{1}+c_{2}=3.2+1.8=5 \ \\ \ \\ a=\sqrt{ c^2-b^2 }=\sqrt{ 5^2-4^2 }=3 \ \text{cm}$
$c=c_{1}+c_{2}=3.2+1.8=5 \ \text{cm}$

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