TRIGO HELP

miNi

Korea (South)2010 Posts

January 11 2008 04:02 GMT

It takes 10 identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?

my god i've been thinking about it for an hour.
i'm usually very strong at math, yet this question boggles me,
what pisses me off more is that the teacher explained it but i was playing tetris on my calculator.

i feel as if i'm missing some information T__T

Equinox_kr

United States7395 Posts

January 11 2008 04:05 GMT

Is it just me or is this question really REALLY badly worded?

miNi

Korea (South)2010 Posts

January 11 2008 04:12 GMT

i think it's pretty clear,

what we've been working on is theta and arc length (s) and such,

edit; fk i dont even know now

ShOoTiNg_SpElLs

Korea (South)690 Posts

January 11 2008 04:25 GMT

since the ten identical pieces form a circular track, draw a circle and divide it into 10 triangular pizza-slice like pieces (? I don't know how else to explain it, it's like an isosceles triangle with an arc at the other end) each of these pieces have an angle of pi/5 at the center.
then draw a smaller circle on the inside (with the same center).
now recall that the formula for arclength is arclength = r * theta, where r is the radius and theta is the angle in radians.

so now if you let the outer arc-length of one of those 10 triangular pieces be x inches, then the inner arc-length of those 10 triangular pieces should be x-3.4.
if you plug this into the formula for arclength, you should be able to find the two radii of the two circles, and the difference is the width of the track.
+ Show Spoiler +

so the radius for the inner circle should be
x-3.4 = r*pi/5
r = (x-3.4) * 5/pi
the radius for the outer circle should be
x = r*pi/5
r = x * 5/pi
so then the difference between the two radii are
3.4*5/pi inches

il0seonpurpose

Korea (South)5638 Posts

January 11 2008 04:29 GMT

Weird how only koreans have posted on this, continue the streak! And I dont think its badly worded, its perfectly fine, I just dont know the answer.

miNi

Korea (South)2010 Posts

January 11 2008 04:41 GMT

thanks i never even attempted using x
챙피하다 ㅜ,.ㅜ

Maenander

Germany4926 Posts

January 11 2008 10:57 GMT

The question is pretty clear and no major explanations are necessary for the solution:

+ Show Spoiler +

width = difference between radii = r1 - r2
difference between the circumferences of the inner and the outer circle:
10*3.4inches = 2pi*r1-2pi*r2 = 2pi*(r1-r2) = 2pi * width
voila

sry for disrupting your korean chain posting

edit: oh didn´t read ShOoTiNg_SpElLs post til the end, he already has the correct answer

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