SOLUTION: In triangle ABC, side AB measures |3x -6| side BC measures |x2-2x| and side AC measures |2x +2| . What is the: i)sine of angle A ii)cosine of angle B iii)tangent of angle A

Algebra ->  Angles -> SOLUTION: In triangle ABC, side AB measures |3x -6| side BC measures |x2-2x| and side AC measures |2x +2| . What is the: i)sine of angle A ii)cosine of angle B iii)tangent of angle A      Log On


   

Question 1184962: In triangle ABC, side AB measures |3x -6| side BC measures |x2-2x| and side
AC measures |2x +2| . What is the:
i)sine of angle A
ii)cosine of angle B
iii)tangent of angle A
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
-----------------------------------
line AB measures |3x -6| line BC measures |x2-2x| and line AC measures |2x +2| .
----------------------------------

No! Not the "lines"; the SEGMENT.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I think you were given that ABC is a right triangle, perhaps with the right
angle at B.  Otherwise, there could be infinitely many solutions.  I'm going
to assume that's what you were given.

If ABC is a right triangle, we can use the Pythagorean theorem, 
assuming AC is the hypotenuse

AB%5E2%2BBC%5E2=AC%5E2

%283x-6%29%5E2%2B%28x%5E2-2x%29%5E2=%282x%2B2%29%5E2

That becomes a 4th degree equation with

x%5E4+-+4x%5E3+%2B+9x%5E2+-+44x+%2B+32+=+0

which has real solutions x=4, and by calculator, 
real irrational solution x≈0.8262208691

So using x=4,

AB=abs%283x-6%29=abs%283%284%29-6%29=abs%2812-6%29=abs%286%29=6
BC=abs%28x%5E2-2x%29=abs%28%284%29%5E2-2%284%29%29=abs%2816-8%29=abs%288%29=8
AC=abs%282x%2B2%29=abs%282%284%29%2B2%29=abs%288%2B2%29=abs%2810%29=10
i)sine of angle A
sin%28A%29=BC%2FAC=6%2F10=3%2F5
ii)cosine of angle B
cos%28B%29=cos%2890%5Eo%29=0
iii)tangent of angle A
tan%28A%29=BC%2FAB=6%2F8=3%2F4

That's one solution.

Using the irrational solution x≈0.8262208691

AB=abs%283x-6%29=abs%283%280.8262208691%29-6%29=abs%28-3.521337393%29=3.521337393

AC=abs%282x%2B2%29=abs%282%280.8262208691%29%2B2%29=abs%283.652441738%29=3.652441738
i)sine of angle A
sin%28A%29=BC%2FAC=0.9698008137%2F3.652441738=0.2655212275
ii)cosine of angle B
cos%28B%29=cos%2890%5Eo%29=0
iii)tangent of angle A
tan%28A%29=BC%2FAB=0.9698008137%2F3.521337393=0.2754069564

That's another solution.

We could also do it assuming AB is the hypotenuse.
We could also do it assuming BC is the hypotenuse.
and,
We could also do it assuming ABC is not a right triangle, 

In the future be sure to copy the problem accurately.
copy it very carefully, then check for typos and omissions.

Edwin