Mathematics HEIGHT & DISTANCE

HEIGHT & DISTANCE

`text(ANGLES OF ELEVATION AND DEPRESSION )`

` (i)text( Angle of elevation :)`
Let `P` be an object and `OX` be a horizontal line; an observer at `O` to perceive the object `P` has to elevate his eye from the direction `OX` to the direction `OP.` As such, we define `angleXOP` as the angle of elevation of `P` at `O.`

`(ii)text( Angle of depression:)`
Let `P` be an object and `OX` be a horizontal line; an observer at `O` to perceive the object `P` has to depress his eye from the direction `OX` to the direction `OP.` As such, we define `angleXOP` as the angle of depression of `P` at `O.`

`(iii)text( Angular elevation :)`
If `PM` is perpendicular to `OX,` then the angle `XOP` is also called the altitude or the `text(angular elevation)` of `MP` at `O.`

`(iv)text( Bearing of a point :)`
Let `NS` and `EW` stand for lines in the north-south and east-west directions respectively then the acute angle which the line `OA` makes with `NS` is called the bearing of the point `A` from `O.`

The bearing of `A` may be indicated precisely, by giving the size of the angle and specifying whether it is measured from `ON (` or `OS)` and whether to east (or west). For example, in figure, `OA` is in the direction `30^0` east of north. Thus, the bearing is written as `N \ \ 30^0\ \ E.`

To express one side of a right angled triangle in terms of other sides

Let `AB = h (`hypotenuse`)` and Let `angleABC = theta.` The side opposite to `theta` is a perpendicular `p` and the remaining side is base `b`

`b =p(cot theta)`

`p = b(tan theta )`

`p= h(sin theta)`

`b = h(cos theta)`

`(a)` If `AD = BE,` then `x = y tan( (alpha + beta)/2)`


`(b)` `h=(asin(alpha+beta))/sin(beta-alpha)`


`(c)` `h=(Hsin(beta-alpha))/(cosalphacosbeta)` and `H=(hcotalpha)/(cosalpha-cosbeta)`

 
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