Indicwiki: 1 revision imported from :alpha:Template:Right_angle_altitude.svg

2023-03-29T03:51:07Z

1 revision imported from alpha:Template:Right_angle_altitude.svg

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alpha>Indicwiki: Created page with "File:right_angle_altitude.svg|thumb|right|The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hy..."

2023-02-03T12:30:51Z

Created page with "File:right_angle_altitude.svg|thumb|right|The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hy..."

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[[File:right_angle_altitude.svg|thumb|right|The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hypotenuse is split into. Using [[Pythagoras' theorem]] on the 3 triangles of sides {{nowrap|(''p'' + ''q'', ''r'', ''s'' )}}, {{nowrap|(''r'', ''p'', ''h'' )}} and {{nowrap|(''s'', ''h'', ''q'' )}},<br style="margin-bottom:1ex;" />
<math>\begin{align}
(p + q)^2 \;\; &= \quad r^2 \;\;\, + \quad s^2 \\
p^2 \!\!+\! 2pq \!+\! q^2 &= \overbrace{p^2 \!\!+\! h^2} + \overbrace{h^2 \!\!+\! q^2} \\
2pq \quad\;\;\; &= 2h^2 \; \therefore h \!=\! \sqrt{pq} \\
\end{align}</math>]]

Template:Right angle altitude.svg - Revision history

Indicwiki: 1 revision imported from :alpha:Template:Right_angle_altitude.svg

alpha>Indicwiki: Created page with "File:right_angle_altitude.svg|thumb|right|The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hy..."