Hello, prashantvrm!

They used "nice" angles in these problems.

We can solve them without a calculator.

. . I'll walk through the first one.

1) As observed from the top of a 100 m lighthouse,

the angles of depression of two ships approaching it are 30° and 45°.

If one ship is directly behind the other, find the distance between the two ships. Code:

A * - - - - - - - - - - - C
| * * 30°
| * *
| * *
100 | * *
| * *
| 45° * 30° *
* - - - - - - * - - - - - - *
B y P x Q

The lighthouse is

The ships are at and

, hence:

, hence:

Let

In .[1]

In .[2]

Substitute [1] into [2]: .

. . Therefore: .