a father and his son are waiting at a bus stop in the evening . there is a lamp post behind them . the lamp post , the father and his son stand on the same straight line . the father observes that the shadows of his head and his son ’ s head are incident at the same point on the ground . if the heights of the lamp post , the father and his son are 6 metres , 1.8 metres and 0.9 metres respectively , and the father is standing 2.1 metres away from the post , then how far ( in metres ) is the son standing from his father ?
explanation : l is the lamp post position , f is father and s is son ’ s position . x is the point where the shadow falls . ld = 0.9 = son ’ s height , lb = 1.8 = father ’ s height . so ab = 6 – 1.8 = 4.2 also bc = lf = 2.1 we observe that ∆ abc ~ ∆ ade ( two triangles are similar ) . hence , the corresponding sides are proportional . so , ab / ad = dc / de . 4.2 / 5.1 = 2.1 / de . de = 5.1 * 2.1 / 4.2 = 5.1 / 2 = 2.55 . ls = de = 2.55 fs = ls – lf = 2.55 – 2.1 = 0.45 . answer : d
divide(multiply(0.9, 2.1), subtract(6, 1.8))