A ladder a = 11 m long is leaning against a wall. If the lower end of the ladder slides away from the wall at the rate of b = 0.5 mls, at what rate is the inclination 6 of the ladder with respect to the ground changing when the lower end is 5 In from the wall? (Use symbolic notation and fractions where needed.) wall ladder In AABC a= licm Let length of BC Cie distance blue B bottom of call and bottom of ladder ) 6 be 'x' em at any instant . Now COBO= BC - AC 11 12 = 11 1010. differentiating both side wirt time ( ". dx d ( 11 1080 ) d+ dx 11 d ( cato ) = 11 ( - sino ). do dt ax = - 11 . sino . de d+ d+ ladder walls all Now, when distance blo foot OF C' of wall a foot of ladderin 5 CM B ' 5 b then (OKO = B'C' A'CI Sing - 1 1- 10120 9 6 F 4 56 11 du = rate of ladder moving away from the wall = 05mpSo , dx - - ll sing . do dt = 0 .5 = - 11 ( 456 ) do do O.5. 4 56 856 Rate of change of inclination of ladder : rad/ 8 856 or o. 051 rad sec. The angle of inclination is reducing at rad 18 or 856 0 . 051 rad / sec