
1 Attachment(s)
tan (αβ)
finding the exact value of tan (αβ) when:
tan α = (5/12) in quad II and cos β = 3/4 and lies in quad I
Triangle α
x = 12
y = 5
r = 13
Triangle β
x = 3
y = √7 (suppose to be square root of 7)
r = 4
tan (αβ) = (tan α  tan ß) / 1 + tan (α) tan (ß)
tan (αβ) = ((5/12)  (√7/4)) / 1 + (5/12)(√7/4)
tan (αβ) = ((5/12)  (3√7/12)) / (48/48) + ((5√7)/48)
tan (αβ) = ((53√7)/12)((48)/(485√7)
tan (αβ) = 1/4 (is what I eventually came up with but it's wrong :( and I am unsure of what I'm doing wrong...)
I've also added a screen shot of the actual equation just in case the above is too confusing...

Re: tan (αβ)
Hello, Ashz!
We are given: .
We have: .
Rationalize: .
. . . .

Re: tan (αβ)
Thanks for replying back ~ but I have 2 additional questions.
1. before we rationalize, how did you get from the tan (αβ) equation to the (1512√7)/(365√7) ~ you multiplied it the whole equation by 36/36 right?
2. then when you rationalize the equation with 36+5√7 ~ this might be an algebra question, and I've probably forgotten, but why can't you just multiply by 5√7 instead of what you have?

Re: tan (αβ)
2 If you just multiply by 5root7 there will still be a root in the denominator so you wont have rationalized it.

Re: tan (αβ)
Sorry :( but now Im confused ~ bc I thought that you would have to rationalize the denominator if there is a square root there... b/c if I didn't have to rationalize it in the first place, why even bother multiplying it by the 5√7 in the first place... or even the 36+5√7...

Re: tan (αβ)
The question didn't say we had to rationalize so we could have left the answer as we had it earlier

Re: tan (αβ)
I'm sorry, but I think your causing me more confusion on this question :( Sorban rationalized the answer and I know I didn't post to rationalize the answer, but the attachment I posted showed that it needed to be rationalized. I am prob the one that caused the confusion on this question, but I tried to minimize it with posting the attachment. I think I will just PM Sorban for more information, thanks for your help anyway biffboy. I do appreciate it.