Q. 184.0( 4 Votes )

# As observed from the top of a lighthouse, 200 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.

Answer :

**To find:**

The distance travelled by ship.

**Formula Used:**

**Explanation:**

Let A and B be two positions of the ship.

Let d be the distance travelled by the ship i.e. AB = d metres

PO = 200 metres

∴ ∠OAP = 30° and ∠OBP = 45°

In Δ OPB,

⇒ BP = 200 m

In ΔOPA,

⇒ d + BP = 200√3

⇒ d + 200 = 200√3

⇒ d = 200√3 – 200

⇒ d = 200(√3 – 1)

⇒ d = 200(1.732 – 1)

d = 146.4 m

Hence distance travelled by ship is 146.4 m.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSThe pillars of equal height stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevation of the top of the pillar are 60° and 30° . Find the height of the pillars and the position of the point.NEXTIf the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then find the height of the cloud above the lake.

Related Videos

Quiz | Applications of Trigonometry47 mins

Application of Trigonometry45 mins

Champ Quiz | Trigger on Trigonometry47 mins

Basics of TrigonometryFREE Class

Fundas of Trigonometry50 mins

NCERT | Trigonometric Identities52 mins

NCERT | Imp. Qs. on Trigonometry42 mins

Quiz | Trail of Mixed Questions on Trigonometry59 mins

Champ Quiz | NTSE Trigonometry50 mins

Testing the T- Ratios of Specified Angles57 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation