Calculating the length of the altitude of a right triangle

OPPOSITE: 500
ADJACENT: 250
HYPOTENUSE: 559.016994374947424102293417182688

ALTITUDE:  223.606797749978969640917366873155
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How to calculate the HYPOTENUSE:

HYPOTENUSE = SQRT(OPPOSITE^2 + ADJACENT^2)
=======================
How to calculate the ALTITUDE:

The altitude of a right triangle disects the right triangle into two right triangles
that anomalously have the same ratios as the right triangle it disects.

Therefore, knowing the length of the OPPOSITE and the ADJACENT (which are the hypotonii
of the two triangles produced by disecting the right triangle by the ALTITUDE) is enough
to calculate the length of the ALTITUDE.

ADJACENT = HYPOTENUSE 1
OPPOSITE = HYPOTENUSE 2

Given that the two RIGHT TRIANGLES produced by disecting the RIGHT TRIANGLE by the ALTITUDE
share the ALTITUDE as either the OPPOSITE or the ADJACENT of the two RIGHT TRIANGLES produced
by disecting the RIGHT TRIANGLE by the ALTITUDE. Therefor for one of those RIGHT TRIANGLES
produced by disecting the RIGHT TRIANGLE with the ALTITUDE is the OPPOSITE, and for the other
RIGHT TRIANGLE produced by disceting the RIGHT TRIANGLE with the ALTITUDE, the ALTITUDE is
the ADJACENT.


OPPOSITE OF TRIANLGE A = ALTITUDE
ADJACENT OF TRIANGLE B = ALTITUDE


TRIANGLE A
HYPOTENUSE = 250
OPPOSITE = ALTITUDE
ADJACENT = UNKNOWN

TRIANGLE B
HYPOTENUSE = 500
OPPOSITE = UNKNOWN
ADJACENT = ALTITUDE

The ratio of the HYPOTENUSE of the RIGHT TRIANGLES produced by disecting the RIGHT TIRANGLE
with the ALTITUDE are exactally the same as the HYPOTENUSE of the RIGH TRIANGLE that is disceted
by the ALTITUDE.

IE:
HYPOTENUSE / (TRIANGLE A HYPOTENUSE (ADJACNET)) = RATIO A
HYPOTENUSE / (TRIANGLE B HYPOTENUSE (OPPOSITE)) = RATIO B

OPPOSITE: 500
ADJACENT: 250
HYPOTENUSE: 559.016994374947424102293417182688

ALTITUDE:  223.606797749978969640917366873155

RATIO A = 559.016994374947424102293417182688 / 250
RATIO B = 559.016994374947424102293417182688 / 500

RATIO A = 2.236067977499789696409173668731
RAITO B = 1.118033988749894848204586834366


To calculate the ALTITUDE, we use (HYPOTENUSE A / RATIO B) or (HYPOTENUSE B / RATIO A)

Which produces the:
OPPOSITE of TRIANGLE A
and the
ADJACENT of TRIANGLE B


To calculate the:
ADJACENT of TRIANGLE A
and the
OPPOSITE of TRIANGLE B

We use:
(HYPOTENUSE A / RATIO A)
and
(HYPOTENUSE B / RATIO B)
=======================
(500 / 559.016994374947424102293417182688) * 447.21359549995793928183473374611 = 400
(250 / 559.016994374947424102293417182688) * 111.803398874989484820458683436578 = 50
=================
EQUATIONS:
OPPOSITE = 500
ADJACENT = 250
HYPOTENUSE = SQRT(OPPOSITE^2 + ADJACENT^2)

ALTITUDE = ADJACENT / (HYPOTENUSE / OPPOSITE)
ALTITUDE = OPPOSITE / (HYPOTENUSE / ADJACENT)

OTHER A = ADJACNET / (HYPOTENUSE / ADJACENT)
OTHER B = OPPOSITE / (HYPOTENUSE / OPPOSITE)

JACNET OPPOSITE = OPPOSITE / HYPOTENUSE * OTHER A
OPPOSITE JACENT = ADJACNET / HYPOTENUSE * OTHER B