Altitude identities in a non-right triangle

Altitude identities in a non-right triangle

Secondary 2
8 marks
TGM Original Questions

Core stretch

In \(\triangle ABC\), \(AC=10\) cm, \(BC=8\) cm and \(AB=12\) cm. The perpendicular from \(C\) meets \(AB\) at \(N\). Let \(AN=a\), \(BN=b\), \(CN=h\).

  1. Express \(a^2\) in terms of \(h\).[2]
  2. Express \(b^2\) in terms of \(h\).[2]
  3. Find \(a^2-b^2\).[2]
  4. Find \(a-b\).[2]

Solution:

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Answer:(i) \(100-h^2\) (ii) \(64-h^2\) (iii) \(36\) (iv) \(3\) cm.

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