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Trigonometry How far above the ground is the tack?

veronica1999

Member
Jun 4, 2012
63
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

Well-known member
MHB Math Scholar
Jan 30, 2012
2,502
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.
 
Last edited:

veronica1999

Member
Jun 4, 2012
63
Thank you!!! :D
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

Well-known member
Feb 2, 2012
409
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?} $