# Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.

Result

a =  6 cm
b =  6.708 cm
c =  9 cm

#### Solution:

$a=6 \ \text{cm}$
$c=\sqrt{ a^2+b^2 }=\sqrt{ 6^2+6.7082^2 } \doteq 8.9998 \ \\ c_{ 1 }=c-c_{ 2 }=8.9998-5 \doteq 3.9998 \ \\ x_{ 1 }=a^2-c \cdot \ c_{ 1 }=6^2-8.9998 \cdot \ 3.9998 \doteq 0.002 \ \\ x_{ 2 }=b^2-c \cdot \ c_{ 2 }=6.7082^2-8.9998 \cdot \ 5 \doteq -0.002 \ \\ c=8.9998 \doteq 8.9998=9 \ \text{cm}$

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