SOLUTION: The diagram above (not to scale) shows how an elementary student who is 4 feet tall estimates the height of a lamppost. The student stands 30 feet from the base of the lamppost a

Algebra ->  Equations -> SOLUTION: The diagram above (not to scale) shows how an elementary student who is 4 feet tall estimates the height of a lamppost. The student stands 30 feet from the base of the lamppost a      Log On


   

Question 86095: The diagram above (not to scale) shows how an elementary student
who is 4 feet tall estimates the height of a lamppost. The student
stands 30 feet from the base of the lamppost and measures her
shadow from the light as 6 feet long. Approximately how high is
the lamppost?
A. 20 feet
B. 24 feet
C. 36 feet
D. 45 feet
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the unknown side, we can use proportions to find the missing side.


Since we have 2 similar triangles, the ratio of the sides of the triangles are the same. Since the ratio of the sides of the small triangle are the same, this ratio is true:

4%2F6=x%2F%2830%2B6%29

4%2F6=x%2F36

This basically says: "the ratio of the side with length of 4 to the side of length 6 is equal to the ratio of side x to side 36 (notice the sides of the triangles correspond to one another)

36%284%2F6%29=%28x%2Fcross%2836%29%29cross%2836%29 Multiply both sides by 36

144%2F6=x Multiply

24=x

So the length of the unknown side is 24, which means the lamppost is 24 feet high

So the answer is B)