Without Euclid laws

Right triangle ABC with a right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws.

Correct answer:

h =  11.8

Step-by-step explanation:

$$\begin{gathered} a=14 \\ c=26 \\ {c}^2=a^2+b^2 \\ b=\sqrt{c^2-a^2}=\sqrt{26^2-14^2}=4\sqrt{30}\doteq 21.9089 \\ {S}_1=S_2 \\ \frac{\{}{}ab\}\{2\}=\frac{\{}{}ch\}\{2\} \\ a\cdot b=c\cdot h \\ h=\frac{a\cdot b}{c}=\frac{14\cdot 21.9089}{26}=11.8 \end{gathered}$$

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