Question 326397
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You didn't say (and you really should have) that side *[tex \Large c] is the hypotenuse.  I'm going to assume that because that is the typical way that triangles are labeled.  However, if this assumption is wrong, and therefore my answer is wrong, it is on you for failing to describe the problem fully.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c^2\ =\ a^2\ +\ b^2]


Substitute what you know:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 19^2\ =\ a^2\ +\ (2a)^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 19^2\ =\ a^2\ +\ 4a^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 19^2\ =\ 5a^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ \frac{19}{\sqrt{5}}\ =\ \frac{19\sqrt{5}}{5}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 2a\ =\ \frac{38\sqrt{5}}{5}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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