Application of Sine and Cosine Ratios in Multi-Triangle Systems

Application of Sine and Cosine Ratios in Multi-Triangle Systems

Secondary 3

The diagram shows two triangles, \(\Delta ABC\) and \(\Delta ACD\).
\(\angle CAD = 90{}^\circ\), \(\angle ABC = 25{}^\circ\), \(AD = 4\) cm and \(AB = 8\) cm.
Find

  1. \(\angle ADC\),
  2. the length of \(CD\),
  3. the length of \(BC\).

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Answer:(i) \(57.7^\circ\) (ii) \(7.49\text{ cm}\) (iii) \(1.90\text{ cm}\)

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