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Angle of Elevation and Depression

Let O and P be two points such that P is at higher level than O. Let PQOX be horizontal lines through P and Q, respectively. If an observer (or eye) is at O and the object is at P, then XOP is called the angle of elevation of P as seen from O. This angle is also called the angular height of P fromO.
If an observer (or eye) is at P and the object is at O, then QPO is called the angle of depression of O as seen from P.

Method of solving a problem of height and distance

  1. Draw a figure nearly showing all angles and distances as far as possible.
  2. Always remember that if a line is perpendicular to a plane then it is perpendicular to every line in that plane.
  3. In the problems of height and distances we come across a right-angled triangle in which one (acute) angle and a side is given. Then to find the remaining side, use trigonometrical ratios in which known (given) side is used, i.e., use the formula.
  4. In any triangle other than right-angled triangle, we can use “the sine rule”, i.e., formula, a/sin A = b/sin B = c/sin C, or cosine formula, i.e., cos A = (b2 + c2 – a2)/2bc etc.
  5. Find the length of a particular side from two different triangles containing the side common and then equating the two values thus obtained.

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