Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. he places a standard 12 inch ruler next to the goal post and measures the shadow of the ruler and the background. if the ruler had a shadow of 10 inches and the backboard has a shadow of 7.25 feet, then how high is the top of the backboard

7.91

Step-by-step explanaton:

  Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 11 inches and the backboard has a shadow of 7.25 feet, then about how high is the top of the backboard?

A.  

6.14 feet

 B.  

8.92 feet

 C.  

7.91 feet

D.  

9.17 feet

i was looking for the answer and jess couldn't find it and so i answered it and it told me the answer was 7.91.

it also told me that the reason for this was:

Since the backboard and the ruler are both vertical and the sun is at the same position in the sky, the triangle made by the backboard and its shadow is similar to the triangle made by the ruler and its shadow.

The ratio of the corresponding sides of the triangles are equal and the height of the backboard can be determined by solving the following proportion.

Therefore, the top of the backboard is 7.91 feet high.