Question

A tower is 50 m high. When the sun’s altitude is 45° then what will be the length of its shadow?

Answer 1

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Answer 2

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:
BC = 50 m(the height of the tower)
∠BAC = 45°

Let AB x m be length of the Shadow of the tower.

In ∆ABC ,
tan 45° = BC / AB = P/ B
1 = 50 / AB
AB = 50 m

Hence , the length of the Shadow of the tower is 50 m.

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