Similar triangles

Question

A lamp post is 6 meters high and placed on flat ground. A person 1.6 meters tall stands at a distance of x meters from the base of the post and sees his shadow just touching the lamp post's shadow. Knowing that the person's shadow is 2.4 meters long, calculate the distance from that person to the lamp post.

Albert Burgess - monkey mart

Answer 1

construct 2 similar right triangles, one inside the other

larger has height 6 meters and base = x +2.4 meters

smaller has base 2.4 meters and height 1.6 meters

(x+2.4)/6 = 2.4/1.6 = 3/2 = ratio of base to height for both triangles

(x+2.4)/6 = 3/2

divide both denominators by 2

(x+2.4)/3 = 3/1

cross multiply

x +2.4 = 9

x = 6.6 meters = distance of man to bottom of the lamp post

Answer 2