How to solve the problem of Heights and Distances?

Understand Height and Distance with a numerical problem. Click on the link to Watch the VIDEO explanation: Watch Video

Problem on Heights and Distances
An observer on the top of a cliff 200 m above the sea level, observes the angles of depression of thr two ships to be 45 degrees and 30 degrees respectively. Find the distance between the ships, if the ships are  
1.        On the same side of the cliff
2.        On the opposite sides of the cliff
Click on the buttons for the solution
The first case, ships on the same side of the cliff. 
Solution
Observe the picture carefully
In the figure cliff AB is equal to 200 m. C and D are the positions of the two ships. It is required to find the length of CD,  that is the distance between the two ships. In right angled triangle ABC, tan 45 is equal to 200 by BC, which implies that 1 is equal to 200 by BC. Calculate the value of BC and click on the OK button.
In right angled triangle ABD, tan 30 is equal to 200 by BD, which implies that 1 by root 3 is equal to 200 by BD. Therefore BD is equal to 200 into root 3, that is equal to 200 into 1.73. calculate the value of BD and click on the OK button.
Therefore the distance between the ships is equal to CD that is equal to BD minus BC that is 346 minus 200. Calculate the distance between the ships and click on the Ok button.
The second case when ships are on the opposite sides of the cliff.
Solution
Observe the picture carefully
In the figure the distance between the two ships is equal to CD which is equal to BD plus BC that is equal to 346 plus 200. Calculate the value and click OK.