# Angle of Elevation and Depression

Let

*O*and*P*be two points such that*P*is at higher level than*O*. Let*PQ*,*OX*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*from*O*.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

- Draw a figure nearly showing all angles and distances as far as possible.
- Always remember that if a line is perpendicular to a plane then it is perpendicular to every line in that plane.
- 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.
- 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*= (*b*^{2}+*c*^{2}–*a*^{2})/2*bc*etc. - Find the length of a particular side from two different triangles containing the side common and then equating the two values thus obtained.