In a given right triangle
, the hypotenuse
, of length
, is divided into
equal parts (
and odd integer). Let
be the acute angel subtending, from
, that segment which contains the mdipoint of the hypotenuse. Let
be the length of the altitude to the hypotenuse fo the triangle. Prove that:
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In a given right triangle $ABC$, the hypotenuse $BC$, of length $a$, is divided into $n$ equal parts ($n$ and odd integer). Let $\alpha$ be the acute angel subtending, from $A$, that segment which contains the mdipoint of the hypotenuse. Let $h$ be the length of the altitude to the hypotenuse fo the triangle. Prove that: $$\tan{\alpha}=\dfrac{4nh}{(n^2-1)a}.$$
Školjka