a person who is 6 feet tall walks away from a 50-foot silo toward the tip of the silo's shadow . at what distance of 32 feet from the silo, the person's shadow begins to emerge beyond the silo's shadow
Let the distance from the tip of silo's shadow and the man is a feet,Let the 50 feet silo is AB,and the 6 feet man is CD, Let the position of the silo's shadow tip is E, Given AC = 32 feet =>AE = 32 + a =>In triangle ABE:- =>tanE = AB/AE = 50/(32+a) --------(i) =>In triangle CDE:- =>tanE = CD/CE = 6/a ----------(ii) on equating (i) (ii):- => 50/(32+a) = 6/a =>50a = 192 + 6a =>44a = 192 =>a = 192/44 = 4.36 feet is the required answer.
Subtract the man's height from the silo's. (50 - 6) = 44 ft. Tan angle at top of triangle = (32/44), atn = 36 deg. Using this angle, find length of base of triangle for shadow length from 50 ft. silo. Tan 36 x 50 = 36.365 ft. 36.365 - 32 = 4.365 ft. further.
