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Question
A pole of height 30 m is observed from a point. The angle of depression of the point is 30°. Find the distance of the point from the base of the pole.
Solution
Let XY be the pole and Z be the position from which the pole is observed.
MXZ and ∠XZY are alternate angles.
Now, in ΔXYZ,
tan 30° = `(XY)/(YZ)`
⇒ `1/sqrt(3) = 30/(YZ)`
⇒ YZ = `30sqrt(3)`
As a result, the distance between point Z and the pole's base is `30sqrt(3)` m.
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