Question

A small wheel resting against an "edge", the height of which is 2 cm, and the distance from the point where the wheel stands on the floor to where it meets the "edge" is 5 cm. What is the radius of the wheel?

Answer 1

Thinking about this as a right triangle, you can conclude that the 2 lies next to the right angle, or "edge." Now 5 is the distance from where the wheel touches the floor to the "edge," so 5 also lies next to the right angle. All you need is the hypotenuse using the pythagorean theorem:

a^2+b^2=c^2

A and B being sides adjacent to the right angle.

Does this make sense?

Answer 2

Use pythagorean theorem and solve for 'r' like @flixoe suggested.

@Stonex

Answer 3

Yeah, but it doesn't exactly look like that, maybe I should have included a diagram from the start

Answer 4

Yeah you'll need a diagram, because as is, it's pretty confusing.

Answer 5

Sorry for the flawed diagram but you get the point

Answer 6

Oh I see what you're saying. @Stonex Is your point that the edge isn't in fact tangent to the circle which is why the 'r' is actually slightly shorter than the radius?

Answer 7

Yes

Answer 8

Should've included that from the start, but it was for some reason not included where I found the question, only in the diagram, I still should have made that point clear though

Answer 9

@Stonex I am pretty confident that the image is probably not accurately made and it's simply a flaw. It's kind of obvious to see that this question requires the application of the pythagorean theorem by how its constructed. Also, if what you're saying is correct, then there is no way to solve this problem since there isn't enough information given. Therefore, I can be very sure that this problem requires the pythagorean theorem to be applied just the way I showed in the above posted picture.

Answer 10

I think i have to agree with genius, I'm not sure the the radius is solvable as is (as in there's no specific value of r).

Answer 11

That was what I thought too, though I found it on a official practice paper for a mathematics competition in my country, seems strange that there would be a simple mistake such as this, and that the presumably correct version of it would have such as simple solution

Answer 12

Find the 23 degree angle using sine, then subtract it from 90 to get the other angle, since it's a tangent (the circle on the floor, so the radius and forms a right angle with the floor)

Then use the cosine rule to find r\[\Large r^2 = 5^2 + r^2 - 2*5r \cos 66.41\]It's pretty late and i'm tired and lazy (and possibly have done something wrong) so: http://www.wolframalpha.com/input/?i=r%5E2+%3D+5%5E2+%2B+r%5E2+-+10rcos66.41&a=TrigRD_D

r = 6.24