3D Trigonometry: Solving Angles of Elevation in a Non-Right Triangular Field

3D Trigonometry: Solving Angles of Elevation in a Non-Right Triangular Field

Secondary 3

The diagram above shows a triangular field \(ABC\). \(AB=45\) m, \(BC=28\) m and angle \(ABC\) is a right angle.
Calculate

  1. angle \(BAC\),
  2. length \(AC\).

A pole \(AD\) is planted perpendicular to the ground such that the angle of elevation of \(D\) from \(B\) is \(40{}^\circ\).
Calculate

  1. the height of the pole,
  2. the angle of elevation of \(D\) from \(C\),
  3. the area of triangle \(BDC\).

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Answer:(i) \(\angle BAC=31.9^\circ\) (ii) \(AC=53\text{ m}\) (iii) \(AD=37.8\text{ m}\) (iv) \(\angle ACD=35.5^\circ\) (v) \(822\text{ m}^2\)

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