# 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.

**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.