James B. answered • 06/11/16
Tutor
5.0
(3,069)
Experienced, Patient, Passionate Geometry Tutor (Inperson and online)
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
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