Expert: Scott A Wilson - 9/24/2009

Question
hey, so I failed geometry my tenth grade year and now I have to make it up online simply because I didn't understand how to do proofs, which I still don't know how to do.
now what is this..
<a href="http://tinypic.com" target="_blank"><img src="http://i36.tinypic.com/2z8z18z.jpg" border="0" alt="Image and video hosting by TinyPic"></a>
In the circle shown, express the ratio 18/19 as the sine, cosine or tangent of an angle measure. Find x to the nearest degree.

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i hope the picture works  

Answer
I have no way of accessing that picture.
When I want to send pictures, they need to be put in a JPG file by a drawing language.
I will send back a basic JPG file which was created in my Paint program and saved as a JPG file.
Note that the file extension had to be chosen.

sine
If 18/19 is the sine of that number,
that means if the far side from the angle is 18, the hypoteneuse if 19.
This makes the near side √(19²-18²) = √(361-324) = √37.
Since 6² = 36, the near side is a little greater than 6.

Call the angle in 0° to 90° x.  Since the sine is positive, the other angle is 180°-x.

cosine
If 18/19 is the cosine of that number,
that means if the near side to the angle is 18, the hypoteneuse if 19.
This makes the far side √(19²-18²) = √(361-324) = √37.
Since 6² = 36, the far side is a little greater than 6.

Call the angle in 0° to 90° x.  Since the cosine is positive, the other angle is 360°-x.

tangent
If 18/19 is the tangent, that means if the far side is 18, the near side is 19.
This makes the hypoteneuse into √(18²+19²) = √(324+361) = √685.
Since 26²=676, the hypoteneuse is a little over 26.

Call the angle in 0° to 90° x.  Since the tangent is positive, the other angle is 180°+x.