Find tan (A - B) for sin A = 12/13 with 0

Question

Find tan (A - B) for sin A = 12/13 with 0 < A < π/2 and cos B = 8/17 with 0 < B < π/2

anonymous · Answer

I would appreciate any help on these review questions: http://imgur.com/eBAAHd2 We're studying for the upcoming final and I'm super nervous! Help would be much appreciated as I could really use some!

anonymous · Answer

I'm tying to figure this out by using the pythagorean theorem with the sum and difference identities, but I'm having a rough time figuring it out.

usukidoll · Answer

hmm.. I think you need one of the identities.

usukidoll · Answer

but I really need to study for my own final and eat dinner... sorry :(

usukidoll · Answer

it has something to do with the identities... that's all I can throw out there

campbell_st · Answer

well for the given information of sin(A) = 12/13

draw a triangle 

|dw:1399270296904:dw|

find x using pythagoras' theorem.... 

then you can find tan(A)

you need to provide some information on B

hope it helps

campbell_st · Answer

and you need another triangle for B

|dw:1399270423602:dw|

find y using pythagoras' theorem... 

then you can find tan B

and the expansion of 

$$\tan(A - B) = \frac{\tan(A) - \tan(B)}{1 + \tan(A)\tan(B)}$$

so substiute your ratios and evaluate

anonymous · Answer

@campbell_st Thanks! I figured that would be the formula we would use. If it would help any, my teacher provided us with this video: http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=7833/7833.xml But our examples are with ratio's and degrees: http://imgur.com/eBAAHd2 However I think I may be able to turn them into degrees.