Question #4a994

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Question #4a994

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Answer 1 · 2017-12-04T20:56:06

A right triangle with the smallest angle of 22.5º ( $\frac{π}{8}$ $pi/8$ rad) will have the other equal to 67.5º ( $3 \frac{π}{8}$ $3pi/8$ rad ). The proportions are fixed:

For a catete with length $a$ $a$ will we have the other catete:

$b = a tan (\frac{π}{8}) = a (\sqrt{2} - 1)$ $b=atan(pi/8)=a(sqrt(2)-1)$

$(\sqrt{2} - 1) = \frac{a}{b}$ $(sqrt(2)-1)=a/b$

Since $(\sqrt{2} - 1)$ $(sqrt(2)-1)$ is an irrational number it cannot be found by the ratio between two integer numbers, so the problem doesn't have solution

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Question #4a994

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