Question

In the figure, two persons are standing at the opposite direction P & Q of the tower. If the height of the tower is 60 m then find the distance between the two persons.

Answer 1

LINE OF SIGHT: The line of sight is a line drawn from the eye of an observer to the point in the object viewed by the observer.

ANGLE OF ELEVATION: The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal , when it is above the horizontal level.

ANGLE OF DEPRESSION:The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal , when it is below the horizontal level.

•Angle of elevation and depression are always acute angles.

•If the observer moves towards the perpendicular line(Tower/ building) then angle of elevation increases and if the observer move away from the perpendicular line(Tower/ building) angle of elevation decreases.

SOLUTION:
GIVEN:
AB = 60 m , ∠APB = 30°, ∠AQB = 45°

Let PB = x m & BQ = y m

In ∆ ABP,
tan 30° = P/B = AB/PB
1/√3 = 60/x [tan 30° = 1/√3]
x = 60√3 m

In ∆ ABQ,
tan 45° = P/B = AB/BQ
1 = 60/y [tan 45° = 1]
y = 60 m

PQ = PB + BQ
PQ = x + y
PQ = 60√3 + 60
PQ = 60(√3 + 1) m

Hence, the distance  between the two persons is 60(√3 + 1) m.

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