shadow problem

Question

Shadow Math
Jeannie is practicing on
the basketball goal outside her house. She thinks that the
goal seems lower than the 10 ft. goal she plays on in the gym. She wonders how far
the goal is from the ground. Jeannie can not reach the goal to measure the distance
to the ground, but she rememb
ers something from math class that may help. First,
she needs to estimate the distance from the bottom of the goal post to the top of the
backboard. To do this, Jeannie measures the length of the shadow cast by the goal
post and backboard. She then stands
a yardstick on the ground so that it is
perpendicular to the ground, and measures the length of the shadow cast by the
yardstick. Here are Jeannie’s measurements:
Length of shadow cast by goal post and backboard: 5 ft. 9 in.
Length of yardstick’s shadow:
1 ft. 6 in.
Draw and label a picture to illustrate Jeannie’s experiment. Using her measurements,
determine the height from the bottom of the goal post to the top of the backboard.
If the goal is approximately 24 inches from the top of the backboard, ho
w does the
height of the basketball goal outside Jeannie’s house compare to t

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