Question

From the top of the Eiffel Tower, a jogger is spotted heading toward the tower. When at position A, the angle of depression of the jogger was measured to be 37. A few minutes later, when measured at position B, the joggers angle of depression had increased by 35 (to a total of 72). Find the distance AB

Answer 1

325 meters if using full height of 324 meters for tower 
277 meters if using observation platform height of 276 meters.  
When the depression is 37 degrees, you can create a right triangle with the angles 90, 37, and 53 degrees. The distance from a point directly underneath the observer will be:
 h/tan(37)
 where
 h = height of the observer.
 
 And when the depression is 72 degrees, the distance will be:
 h/tan(72) 
 So the distance between the two points will be the absolute value of:
 h/tan(72) - h/tan(37)
 =(tan(37)h)/tan(37)tan(72) - tan(72)h/(tan(37)tan(72))
 =(tan(37)h - tan(72)h) /(tan(37)tan(72))
 =h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
 =h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
 =h(-2.324129487/2.319200894)
 =h*-1.002125125
 
 And since we're looking for absolute value
 =h*1.002125125
 
 As for the value of "h" to use, that's unspecified in the problem. If you take h
to be the height of the Eiffel Tower, then it's 324 meters. If you take h to be
the highest observation platform on the Eiffel Tower, then it's 276 meters. In
any case, simply multiply h by the value calculated above:
 =h*1.002125125
 =324*1.002125125
 = 324.6885406 m
 
 =h*1.002125125
 =276*1.002125125
 =276.5865346