Trigonometry How far above the ground is the tack?

[veronica1999]

Devon's bike has wheels that are 27 inches in diameter. After the front wheel picks up a tack, Devon rolls another 100 feet and stops. How far above the ground is the tack?

I did all my work carefully but the answer seems wierd.

circumference of tire :84.78 inches
total distance traveled is 1200 inches

1200 /84.78 = 14.154

84.78 : 0.154 = 360: X

X = 0.653

13.5cos0.653 = 13.4991

13.5 - 13.4991 = 0.000876

answer : 0.000876

 

[Evgeny.Makarov]

First, it would help to use more digits of pi. Then 1200/(27$\pi$)=14.147 up to 3 decimal digits.

84.78 : 0.154 = 360: X

This should be X / 360 = 0.147 (this is a fraction of the full circle). Then X = 52.958 degrees and the final answer is 5.368 inches.

 

[veronica1999]

Thank you!!!
Now I see my mistake.

Instead of 84.78 : 0.154 = 360 : X
the equation should have been 84.78 :13.056 = 360 :X
X = 55.4

1200/27pi = 14.147

84.78 : 12.46 = 360 :X
x= 52.958

 

[soroban]

Hello, veronica1999!

Devon's bike has wheels that are 27 inches in diameter.
After the front wheel picks up a tack, Devon rolls another 100 feet and stops.
How far above the ground is the tack?

I did all my work carefully but the answer seems weird.

Circumference of tire: 84.78 inches . This is wrong.
Total distance traveled is 1200 inches

1200 / 84.78 = 14.154

84.78 : 0.154 = 360 : X . This is wrong, too.

X = 0.653 . That is a VERY small angle, isn't it?

13.5cos0.653 = 13.4991

13.5 - 13.4991 = 0.000876

Answer: 0.000876

$\text{Circumference: }\:27\pi \:\approx\:84.82 $

$ \text{Then: }\:\dfrac{1200}{84.82} \:=\:14.1476\text{ revolutions} $

$\text{The wheel makes 14 revolutions and a fraction of a revolution.}$

$\text{That fraction is: }\:0.1476 \times 360^o \:=\:53.136^o $

$\text{Got it?} $