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![Right Triangles Formulas](../machu_picchu_h1_910.jpg)
How to Master Right Triangle Math: From Pythagoras to 3-D Coordinates
Comprehensive coverage of right triangle formulas, including the Pythagorean theorem, catheti, hypotenuse, altitude, projection, inradius, circumradius, exradius, semiperimeter, area, special right triangles, Poncelet's theorem,
general extension, and 2-D coordinates, as well as the Pythagorean theorem in 3-D.
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PYTHAGOREAN THEOREM, GEOMETRIC
MEAN, PRODUCT OF THE CATHETUS, ALTITUDE, PROJECTION:
Proofs that use
similarity.
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SPECIAL RIGHT TRIANGLES:
Isosceles 45-45, 30-60, 37-53 (3-4-5)
![Special Right Triangles 45, 30, 60,37,53 degrees](right_triangle_special.gif)
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CENTERS, INRADIUS,
CIRCUMRADIUS, INCENTER, CIRCUMCENTER, ORTHOCENTER, CENTROID,
PONCELET'S THEOREM, SAGITTA.
Sagitta: The distance
between the midpoint of an arc and the midpoint of its
chord.
![Right Triangle Formulas](right_triangle_inradius.gif)
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RIGHT TRIANGLE:
INRADIUS, EXRADII, SEMIPERIMETER (s), CATHETUS AND
HYPOTENUSE, AREA.
![Right triangle formulas](right_triangle_exradius.gif)
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RIGHT TRIANGLE: ORTHOGONAL
PROJECTIONS
![Right triangle, projection facts](right_triangle_projection.gif)
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RIGHT TRIANGLE: ALTITUDE,
INRADII, INCENTER, AREAS.
![Right triangle, altitude facts](right_triangle_altitude.gif)
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PYTHAGOREAN THEOREM: DIAGONAL OF A BOX
![Pythagorean theorem: Diagonal of a box](right_triangle_box.gif)
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DISTANCE IN CARTESIAN
COORDINATE:
The Pythagorean Theorem provides
an easy way to compute the straight line distance between
any two points whose Cartesian coordinates are known.
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PYTHAGOREAN THEOREM IN THREE DIMENSIONS 3-D, De Gua's
Theorem: In any
tetrahedron with a cubic vertex O-ABC the square
of the area of the face opposite the cubic vertex O-ABC is
equal to the sum of the squares of the areas of
the other three faces AOB, AOC, BOC.
![Pythagoras theorem 3-D](pythagoras_3D.gif)
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THE PYTHAGOREAN CURIOSITY: Triangles and squares, fifteen conclusions.
![Pythagoras curiosity. Online tutoring.](pythagoras_curiosity_17.jpg)
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THE GENERAL EXTENSION TO
PYTHAGORAS' THEOREM: If any 3 similar shapes are drawn
on the sides of a right triangle, then the area of the shape
on the hypotenuse equals the sum of the areas on the other
two sides.
![Pythagoras Theorem Extension](right_triangle_similar.gif)
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