Question

a person standing 20 feet from a street light casts a shadow as shown. how many times taller is the streetlight than the person? assume the triangles are similar.

Answer 1

The diagram below shows models the position of each object and its distance

We have two similar triangles; triangle ABC and triangle DBE

We can work out the scale factor of the two triangles by checking the corresponding lines

We have line EB correspond to line CB
The scale factor is EB ÷ CB = 30 ÷ 10 = 3

Line EB is 3 times longer than line CB
So, line DE is 3 times longer than line AC

The street light is the line DE and the person standing is the line AC
So, the street light is 3 times taller than the person standing.

 

Answer 2

Using the concept of similar triangles to calculate the scale factor, the height of the streetlight is 3 times the height of the person.

Length of shadow cast = 10 feets

Height of person = 6 feets

Distance of person from streetlight light = 20 feets

Since the triangles are similar :

Comparing the length of both triangles :

• Bigger triangle = 30 feets
• Smaller triangle = 10 feets

The scale factor is :

• (Bigger triangle / Smaller triangle) = (30/10) = 3
• Therefore, the scale factor is 3

Using the scale factor ; the height of the streetlight will be :

• Height of person × 3 = 6 feets × 3 = 18 feets

Height of streetlight = 18 feets

Height of person = 6 feets

Therefore, the streetlight is (18/6 = 3) 3 times the height of the person.

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