Euclid3

Calculate the height and sides of the right triangle if one leg is a = 81 cm and the section of hypotenuse adjacent to the second leg c_b = 39 cm.

Correct answer:

a =  81 cm
b =  63.3 cm
c =  102.8 cm
h =  49.9 cm

Step-by-step explanation:

$a=81\text{cm}$

$b=\sqrt{((39+\sqrt{39\cdot 39+4\cdot 81\cdot 81})/2{)}^2-81^2}=63.3\text{cm}$

$$\begin{gathered} a^2=(c-39)c \\ {c}^2-39c-6561=0 \\ c=\frac{39+\sqrt{39\cdot 39+4\cdot 81\cdot 81}}{2}=102.8\text{cm} \\ b=\sqrt{c^2-a^2}=63.32\text{ cm} \end{gathered}$$

$h=\sqrt{c_b\cdot (c-c_b)}=49.9\text{cm}$

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