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Median formula (Posted on 2019-03-10) Difficulty: 3 of 5
A right triangle has legs a and b, and hypotenuse c.

The length of the median to the hypotenuse is (a3b + b3a)1/3.

Find the length of the altitude to the hypotenuse

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution Comment 1 of 1
In our right triangle: a=angle between leg a and hypotenuse c; h=altitude

sin(a)=b/c=h/a    =>   h=ba/c

median lenght=c/2 as is evident if designing the whole rectangle

c/2=(a3b + b3a)1/3=ab(a2 + b2)1/3 =(abc2 )1/3.
As ba=hc

c/2=(hc3)1/3=c*h1/3. Then: 1/2=h1/3.


h is invariant for all triangles that verify that lenght of median

  Posted by armando on 2019-03-13 10:46:14
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