MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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.

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.