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
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
So:
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=1/8
h is invariant for all triangles that verify that lenght of median
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Posted by armando
on 2019-03-13 10:46:14 |
Solution
