Mathematics REVISION OF Height And Distance FOR NDA
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REVISION OF Height And Distance FOR NDA

HEIGHT AND DISTANCE

Height and distance is one of the most important application of trigonometry which helps us to
find the height of any object and distance of objects between points which are not directly measurable.

Line of Sight

When the eye of a person at a point 0 looks at an object P, then the line OP is called the line of sight.

Angle of Elevation

Let P be an object and OX be a horizontal line, an observer at 0 to perceive the object P has to
elevate his eye from direction OX to the direction OP. As such, we define ` ∠XOP` as the angle at
elevation of P at O.

Angle of Depression

Let P be an object and OX be a horizontal line, an
observer at 0 to perceive the object P has to depress his
eye from the direction OX to direction OP. As such,
we define `∠ XOP` as the angle of depression of P at O .

Note • Any perpendicular line to a plane is perpendicular to all
lines lying in the plane.

• Angle of elevation and depression are always acute
angles.

m-n Theorem

If D divides AB in the ratio m : n,

(i) `(m+ n)cot theta = n cot A- m cot B`

(ii) `(m+ n) cot theta = m cot alpha - n cot beta`
 
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