Question

In the figure, find the value of BC.

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:
AE = 100 m , CD = 80 m, ∠AEB = 60°, ∠DEC= 45°

Let BE = x cm , EC = y m

In ∆ABE,
cos 60° = B/H = BE / AE
½ = x /100
2x = 100
x = 100/2
x = 50 m

In ∆ DCE,
tan 45°= P/B
1 = 80/EC
y = 80 m

BC = BE + EC
BC = x + y
BC = 50 + 80
BC = 130 m

Hence, the Length of BC is 130 m.

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