As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

Solution:

Let the height of the lighthouse from the sea level be AB and the ships are C and D.

The angles of depression of the ships C and D from the top A of the lighthouse are 30° and 45° respectively.

Distance between the ships = CD = BD − BC

In ΔABC,

tan 45° = AB/BC

1 = 75/BC

BC = 75

In ΔABD,

tan 30° = AB/BD

1/√3 = 75/BD

BD = 75√3

Distance between two ships CD = BD - BC

CD = 75√3 - 75

= 75 (√3 - 1)

Distance between two ships CD is 75 (√3 - 1) m.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 9

Video Solution:

As observed from the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 13

Summary:

If the angles of depression of two ships are 30° and 45°, as observed from the top of a 75 m high lighthouse from the sea-level and if one ship is exactly behind the other on the same side of the lighthouse, then the distance between the two ships is 75(√3−1) m.

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