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. 

Answer 1

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.