Question

If we know two altitude what is the third altitude to form a triangle

Answer 1

By the formula K=12⋅base⋅heightK=12⋅base⋅height for the area of a triangle, A,B,CA,B,C are the altitudes of a triangle iff K2A,K2B,K2CK2A,K2B,K2C are the sides of a triangle, iff 1A,1B,1C1A,1B,1C are the sides of a triangle, iff the triangle inequalities hold:
  1A<1B+1C1A<1B+1C, 1B<1C+1A1B<1C+1A, and 1C<1A+1B1C<1A+1B.
So the necessary and sufficient bounds are
  11A+1B<C<1∣∣1A−1B∣∣11A+1B<C<1|1A−1B|.

Answer 2

Answer:

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