An aeroplane at an altitude of 200m observes the angle of depression of opposite points on the two banks of a river to be 45 and 60 find the widht of river

  84.5 m

Step-by-step explanation:

It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.

The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:

  Tan = Opposite/Adjacent

Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:

  tan(30°) = OB/OA

  OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m

Likewise, we have ...

  OC = (200 m)·tan(45°) = 200 m

Then the width of the river is the difference between these values:

  BC = OC -OB = 200 m - 115.47 m = 84.53 m

step-by-step explanation:

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