John stands on the bridge and observes that the angles of depression of the banks on opposite sides of river Absyssa are 45º and 60º respectively. The bridge is at a height of 6 m from the banks. Calculate the width of the river Absyssa?

Asked by Topperlearning User | 2nd Nov, 2017, 09:34: AM

Expert Answer:

         
 
In the figure, let A and B represent points on the bank on opposite sides of the river Absyssa, so that AB is its width.
 
P is a point on the bridge at a height of 6 m, that is, DP = 6 m.
 
We have to calculate the width of the river, which is the length of the side AB of triangle APB.
 
Now, AB = AD + DB
 
In the right angled triangle APD, ÐA = 45º
Therefore, we have calculated the width of the river Absyssa to be equal to fraction numerator size 12px 6 open parentheses square root of size 12px 3 size 12px plus size 12px 1 close parentheses over denominator square root of size 12px 3 end fraction m.

Answered by  | 2nd Nov, 2017, 11:34: AM