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Question
The height of an observation tower is 180m above sea level. A ship coming towards the tower is observed at an angle of depression of 30°. Calculate the distance of the boat from the foot of the observation tower.
Solution
Let AB be the tower and C be the position of the ship.
Let the distance of the boat from the foot of the observation tower be x.
In triangle ABC,
tanθ = `"AB"/"BC"`
⇒ `tan 30^circ = 180/X`
⇒ `1/sqrt(3) = 180/X`
⇒ `X = 180sqrt(3) = 180 × 1.732 = 311.76`
Thus , the distance of the boat from the foot of the observation tower is 311.76 or 311.8 m.
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