Can You Help Me Find Angle A? - Understanding Sine Calculation

[TSN79]

The drawing below shows an angle A that I'm suppsosed to find. My book does this;

$$sin A=\frac{530-160}{2\cdot505}=0,366$$

I am not able to follow the logic in how this would give me the sine of A...would love it if someone could help me out!

 

[iNCREDiBLE]

The drawing below shows an angle A that I'm suppsosed to find. My book does this;

$$sin A=\frac{530-160}{2\cdot505}=0,366$$

I am not able to follow the logic in how this would give me the sine of A...would love it if someone could help me out!

Shouldn't it be tan A?

 

[LeonhardEuler]

Are you sure they don't mean tanA? Thats what it seems like.

 

[TSN79]

Not according to my book...

 

[TSN79]

You are able to find the same angle in several places here, I just didn't draw them in, it might be calculated in reference to one of these places...?

 

[LeonhardEuler]

No, that can't be it. You can calculate sin (A) based on this picture to be about .344. It will be the same no matter where you calculate it from. Either the picture or the equation is a misprint.

 

[iNCREDiBLE]

If the book says sin A. Then the picture must look like this:

 

[TSN79]

I've included some more details on the drawing now. I'm not sure, but would the angle on the right wheel also be A? The same number data still applies, the 505 is the difference between the two wheels axles.

 

[radou]

According to the first picture, $$sinA=\frac{185}{\sqrt{505^2+185^2}}$$ ...

 

[TSN79]

But it doesn't really matter if it's sin or tan, the angle is the same, but if one you could only tell me the process of your calculation to find it I'd really appreciate that...

 

[LeonhardEuler]

In the first picture, draw a vertical radius in the upper part of the larger circle. Now extend the bottom line from angle A to meet this radius. This forms a right triangle. The leg adjacent to A has length 505. The length of the opposite side can be calculated because you can see that it is the larger radius minus the smaller radius. That is (1/2)530 - (1/2)160. The tangent of the angle is the opposite over the adjacent side, which, factoring out the (1/2), is the expression given.