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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

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W0lf93

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

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