Question

Sam Is Waking In A Straight Line Towards A Lamp Post Which Is 8 M High. When He Is 12 M Away From The Lamp Post , His Shadow Is 4 M In Length . When He Is 8 M From The Lamp Post , What Is The Length Of His Shadow ?

Answer 1

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Sam Is Waking In A Straight Line Towards A Lamp Post Which Is 8 M High. When He Is 12 M Away From The Lamp Post , His Shadow Is 4 M In Length . When He Is 8 M From The Lamp Post , What Is The Length Of His Shadow

From The Lamp Post , What Is The Length Of His Shadowanswer 3m

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Answer 2

Answer: 2.66 m = 8/3 m = 2 2/3 m

Step-by-step explanation:

We can draw a diagram of this with 2 similar triangles, where the smaller similar triangle overlaps the larger one, with a common angle. Since they are similar, the lengths of their corresponding sides are proportional.

Hence, to determine Sam’s height h, we solve for h:

h/4 = 8/16

=> h/4 = 1/2

=> h = 4/2 = 2 metres tall

As Sam moves to a position that is 8 m from the lamp post, we now have a different situation. Using similar triangles as before, we can now calculate L, the length of the shadow, as such:

L/2 = (L + 8)/8

=> 4L/8 = (L + 8)/8 by the property of equivalence in fractions

=> 4L = L + 8

=> 3L = 8

=> L = 8/3

Hence, the length of his shadow is 8/3 metres.