# Without Euclid laws

Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.

Result

h =  4.82

#### Solution:

$b^2 = c^2 - a^2 \ \\ b = \sqrt{ 19^2 - 5^2} = 18.33 \ \\ \ \\ S_1 = S_2 \ \\ \dfrac{ ab}{2} = \dfrac{ c h }{2} \ \\ ab = c h \ \\ \ \\ h =\dfrac{ ab }{ c} = \dfrac{ 5 \cdot 18.33 }{ 19 } = 4.82$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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