Two buildings face each other. The height of one building is greater than that of the other. The smaller building is 80 m high.

The angles of depression of the top and the bottom of the smaller building from the top of the taller building are 45º and 60º respectively. Find the height of the taller building.

Asked by Topperlearning User | 2nd Nov, 2017, 09:19: AM

Expert Answer:

 
In the given figure, PC denotes the taller building and AB denotes the 80 m tall building.
 
 
We are interested in determining the height of the taller building, I which is., PC
 
 If we look at the figure carefully and observe that PB is a transversal to the parallel lines PQ and BD.
 
Therefore, angleQPB and anglePBD are alternate angles, and are equal.
 
So, anglePBD = 45º. Similarly, anglePAC = 60º.
 
In the right angled triangle PBD, we have
 

Answered by  | 2nd Nov, 2017, 11:19: AM