angles of depression

Question

Sarah is standing on a cliff top and observes the angle of depression to a point A in a deep gorge to be 50 degrees. Sarah then turns in the opposite direction and observes another point B in a second gorge to have an angle of depression of 65 degrees. The points, A and B, are both on the same horizontal level 45m beneath Sarah. Find the distance between A and B

Answer 1

Label the point directly below Sarah as C.

 

Using the Law of Sines:

 

AC / sin 40° = 45 / sin 50

 

And

 

BC / sin 25° = 45 / sin 65°

 

AC + BC = AB