Euclid3

Calculate height and sides of the right triangle, if one leg is a = 81 cm and 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:

$a=81\text{ cm}$

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

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

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

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