Question

If the horizontal distance of the boat from the bridge is 25 m and the height of the bridge is 25 m, then find the angle of depression of the boat from the bridge.

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:
Let BC= 25 m be the height of the bridge.
Let AB= 25 m be Distance of the boat From the bridge.

In ∆ABC, ∠B = 90°
Let ∠ACB = θ
∠ACB = ∠DAC = θ [ alternate angles]
tan θ = AB / BC = P/ B
tan θ = 25 / 25
tan θ = 1
tan θ = tan 45°    [ tan 45° = 1]
θ = 45°

Hence, the  angle of depression  of the boat from the  bridge is 45°.

HOPE THIS WILL HELP YOU...

Answer 2

answer is 45° ......................