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Applications of Trignometry

4 viewed last edited 6 months ago
Ananya Juluri
0

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

Vivekanand Vellanki
3

It helps a lot to start by drawing a figure and mark everything - the angles, the distances, and the points.


Here is what I have drawn.

You can see the light-house, the 2 ships and the angles of depression to the two ships.


A is the top of the light-house, B is the bottom of the light-house, C is the first ship and D is the 2nd ship.


\angle BCA=45 - the angle of elevation same as angle of depression. This implies x (BC) = 75m since the ABC is right isoceles and AB = BC.


Similarly, \angle BDA=30


\tan30=\frac{AB}{AD}=\frac{75}{75+d}


Hope this helps you solve the problem.