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You only need elementary
trigonometry and scalar products
Given any right-angled
triangle DABC
on a sphere of unit radius,
right angled at A, and with
lengths of sides a, b and c,
then Pythagoras' Theorem in
Spherical Geometry is
Prove this result.
Find a triangle containing
three right angles on the
surface of a sphere of unit
radius. What are the lengths
of the sides of your triangle?
Use the Pythagoras' Theorem result
above to prove that all spherical
triangles with three right angles on the unit sphere
are congruent to the one you
found.
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