From a window of a high building the angle of depression of a parked car is 50 .From a window of 15m lower the angle of depression is 42?

Question

how far from the base of the building is the parked car?

Answer 1

Straight line between first window and car defines the hypotenuse of right-angled triangle #1. Line between 2nd window and car forms the hypotenuse of right-angled triangle #2. Both of these triangles share a common base.

 

Let height of first window = O m. Then height of 2nd window = O-15 m.  A = distance of parked car.

 

The tangent of triangle #1 = O/A = tan50.  (1)

Tangent of triangle #2 = (O-15)/A = tan42. (2)

 

Dividing equation (1) by (2) gives O/(O-15) = tan50/tan42.  Solving for O gives 61.4 m. A then is O/tan50 =51.5 m