# Geometry

posted by Ashley

in triaangle ABC, AB=20 cm, AC=15 cm the length of the altitude AN is 12 cm prove that ABC is a right triangle

so far i got that angle ANC is 90 degrees by definition on altitude i got really confused after so can you show me how to answer the question and the soulotion please.

1. Reiny

I will assume that N is on BC.
So you have two right-angled triangles, BNA and CNA.

In BNA, BN^2 = 20^2 - 12^2 , so
BN = 16
in CNA, CN^2 = 15^2 - 12^2
CN = 9
so BC = 25 , and
25^2 = 20^2 + 15^2
so by Pythagoras, we have right angle at A

2. Anonymous

I think its Pythagorean, but thanks I had the same problem for Rsm homework

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