In the village of Hazelton, there was a totem pole 50 m high of which the lower 24 m was carved. According to a clue the treasure was hidden at a point on the ground such that the carved and the uncarved portion of the totem pole subtend equal angles. How far away from the pole should the digging be done in order to be rich?
Total height = 50 m tan α = 24/x tan2 α = 50/x tan2 α = 2tan α /(1 - tan2 α ) 50/x = 2*24/x/{1−(24/x)2} ⇒ 50(x2−576)=48x2 ⇒ 2x2=28800 ⇒ x 2 =14400 or x=120m
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