# How do you convert an angle to a fraction?

• Sep 2nd 2009, 03:58 PM
ineedhelp87
How do you convert an angle to a fraction?
Okay, the question says to find the value of "tan" - I did and it was 40 degrees. But the options are all in fractions... none of which convert to 40. I am stumped... I'm thinking there must be some sort of trick to this that I'm not getting... please help me.
• Sep 2nd 2009, 04:04 PM
skeeter
Quote:

Originally Posted by ineedhelp87
Okay, the question says to find the value of "tan" - I did and it was 40 degrees. But the options are all in fractions... none of which convert to 40. I am stumped... I'm thinking there must be some sort of trick to this that I'm not getting... please help me.

then you made an error. tangent is a ratio ... not an angle.
• Sep 2nd 2009, 04:11 PM
ineedhelp87
Thank you... I just realized my mistake. I feel a bit silly. But I still need help. So, tan is the opposite side over the adjecent side, which in this triangle - http://i32.tinypic.com/11i21as.jpg - is 10/15. How can I convert this?
• Sep 2nd 2009, 04:11 PM
ineedhelp87
Options are square root of 11 / 5, square root of 11 / 6, 5/6, and 6/5.
• Sep 2nd 2009, 04:48 PM
skeeter
Quote:

Originally Posted by ineedhelp87
Thank you... I just realized my mistake. I feel a bit silly. But I still need help. So, tan is the opposite side over the adjecent side, which in this triangle - http://i32.tinypic.com/11i21as.jpg - is 10/15. How can I convert this?

find the opposite side using Pythagoras.
• Sep 2nd 2009, 04:57 PM
ineedhelp87
I did and it was 10...
• Sep 2nd 2009, 05:02 PM
skeeter
Quote:

Originally Posted by ineedhelp87
I did and it was 10...

the opposite side is not 10 ...

$\displaystyle \sqrt{18^2 - 15^2} = \sqrt{99} = 3\sqrt{11}$

$\displaystyle \tan{\theta} = \frac{3\sqrt{11}}{15} = \frac{\sqrt{11}}{5}$