Geometry

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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.

  • Geometry -

    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

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