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Advanced Trigonometry in a Four-Sided Figure

Advanced Trigonometry in a Four-Sided Figure

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The figure shows a quadrilateral \(ABCD\) where \(\angle ABC=\angle ACD=90{}^\circ \). Given that \(AC=7.6\)m, \(\angle BAC=40{}^\circ \) and \(\angle ADC=44{}^\circ \), find

  1. the length of \(AB\),
  2. the length of \(BC\),
  3. the length of \(AD\),
  4. the length of \(CD\),
  5. the perimeter of the quadrilateral \(ABCD\),
  6. the area of the quadrilateral \(ABCD\).

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Answer:(i) \(5.82\text{ m}\) (ii) \(4.89\text{ m}\) (iii) \(10.9\text{ m}\) (iv) \(7.87\text{ m}\) (v) \(29.5\text{ m}\) (vi) \(44.1\text{ m}^2\)

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