Shadow math task

Question

Jeannie is practicing on the basketball goal outside her house. She thinks that the seems lower than the 10 ft. goal she plays on in gym. She wants to know how far it is from the ground but she cant reach the goal to measure it. She estimates the distance from the bottom of the goal post and background. Then she stands a yardstick on the so that it  perpendicular to the ground, and measures the length of the cast by the yardstick.

 

Her measures are: 

'Length of shadow cast by goal post and backboard: 5ft 9in'

'Length of yardstick's shadow:1ft 6in' 

 

Draw and label a picture to illustrate Jeannie's experimen. Usin her measurements determine the height from the bottom of the goal post to the too of the backboard. 

 

If tge goal is approximately 24 inches from the too of the backboard, how does the height of the basketball goal outside of Jeannie's house compare to the one in the gym? Justify your answer.

Answer 1

NOTE: 6 in = .5 ft
9 in = .75 ft

•
|
| 3 FT
| (Yardstick & Shadow)
|
•------------------------•
1.5 FT


•
|
|
| X
|
| (Goal Post and Shadow)
|
•---------------------------------•
5.75 ft

Let X = height of the goal post

The above diagrams represent the legs of 2 right triangles ... I could not draw the hypotenuses

Because these are similar triangles, the sides are proportional.

We can construct a proportion and solve for X.

3/X = 1.5/5.75

Cross multiply

1.5X = 3(5.75)

1.5X = 17.25

Divide by 1.5

X = 17.25/1.5

X = 11.5

The goal post is 11.5 ft high. when you subtract the 24 inches (2 ft) because the goal is that distance from the top,
You have the goal being 9.5 ft from the ground