# trig word problem question

• Jun 15th 2009, 06:03 PM
jlbrpt
trig word problem question
Below is a word problem that is driving me nuts. I'll bet the answer is probably an obvious one but for some reason I'm not making any sense of it. I am asking for help in HOW to solve it, not the actual answer...I'd rather work that out and post the answer so it can be checked. Here is the word problem:

Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 6.9 cm and the radius of the larger wheel is 10.9 cm. Through how many degrees will the larger wheel rotate if the smaller one rotates 108 degrees?

Does the 108 degrees of the smaller circle have any relevance beyond the fact that it should rotate more/faster because it is the smaller one, or is it just a matter of solving the angle using s=ar (s=arc length, a = angle, r = radius)? If that is the case, and s=ar, then a = s/r. s= 360 deg, divided by radius 10.9, = 33.02752294, or roughly 33 degrees.

Or am I completely off base and need to work this from a different perspective?
• Jun 15th 2009, 07:22 PM
aidan
Quote:

Originally Posted by jlbrpt
Below is a word problem that is driving me nuts. I'll bet the answer is probably an obvious one but for some reason I'm not making any sense of it. I am asking for help in HOW to solve it, not the actual answer...I'd rather work that out and post the answer so it can be checked. Here is the word problem:

Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 6.9 cm and the radius of the larger wheel is 10.9 cm. Through how many degrees will the larger wheel rotate if the smaller one rotates 108 degrees?

Does the 108 degrees of the smaller circle have any relevance beyond the fact that it should rotate more/faster because it is the smaller one, or is it just a matter of solving the angle using s=ar (s=arc length, a = angle, r = radius)? If that is the case, and s=ar, then a = s/r. s= 360 deg, divided by radius 10.9, = 33.02752294, or roughly 33 degrees.

Or am I completely off base and need to work this from a different perspective?

You have part of the idea.

You have to assume that the circles touch at only one point at the start of the rotation.
The arc length through 108degrees of the smaller circle

$2r \pi \times \frac{108}{360}= 13.006$

13.006 / 10.9 is the radian measure through which the larger circle rotated.
• Jun 15th 2009, 07:46 PM
Shyam
Quote:

Originally Posted by jlbrpt
Below is a word problem that is driving me nuts. I'll bet the answer is probably an obvious one but for some reason I'm not making any sense of it. I am asking for help in HOW to solve it, not the actual answer...I'd rather work that out and post the answer so it can be checked. Here is the word problem:

Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 6.9 cm and the radius of the larger wheel is 10.9 cm. Through how many degrees will the larger wheel rotate if the smaller one rotates 108 degrees?

Does the 108 degrees of the smaller circle have any relevance beyond the fact that it should rotate more/faster because it is the smaller one, or is it just a matter of solving the angle using s=ar (s=arc length, a = angle, r = radius)? If that is the case, and s=ar, then a = s/r. s= 360 deg, divided by radius 10.9, = 33.02752294, or roughly 33 degrees.

Or am I completely off base and need to work this from a different perspective?

See, the arc length will be the same for both the wheels

for smaller wheel, s = ar

for bigger wheel, s = AR

ar = AR

$108^\circ \times 6.9=A\times 10.9$

$A = 68.36^\circ$

the bigger wheel will rotate $68.36^\circ$