# Thread: Law of Cosines - Negative angle??

1. ## Law of Cosines - Negative angle??

Here's the triangle:

a=8
b=3
c=8

I did the law of cosines for C and got 0.1875. I did the arccos of that, and got 79.19°.

I then did the law of sines for A, and got 2.62444. I did the arcsin of that, and got undefined on my TI-89. I put arcsin(2.62444) in WolframAlpha and got -45.88°.

So... Am I doing something wrong?

2. Originally Posted by BeSweeet
Here's the triangle:

a=8
b=3
c=8

I did the law of cosines for C and got 0.1875. I did the arccos of that, and got 79.19°.

I then did the law of sines for A, and got 2.62444. I did the arcsin of that, and got undefined on my TI-89. I put arcsin(2.62444) in WolframAlpha and got -45.88°.

So... Am I doing something wrong?
I got the same thing for angle C. The law of sines is that a/sinA =c/sinC. Since a and c are the same length their angles must be equal. I don't know where you made your error since you didn't post your work but angle C is definitely 79.19 as well.

3. angle A = angle C, no?
since a=c

therefore it would have the same angle.

duno how you got 2.62444.

$\frac{sin79.19}{8}=\frac{sinA}{8}$

$\frac{sin79.19}{8}*8=sinA$

$\rightarrow sin79.19=sinA$

therefore A=79.19.

btw dont trust WolframAlpha

4. So what do I need to do? I've already found one angle, and I can't find the other two...

5. Originally Posted by BeSweeet
So what do I need to do? I've already found one angle, and I can't find the other two...
Like we said, the law of sines should show that the angles opposite the legs with length of 8 are the same. The total angle measure of a triangle is 180, so if you know 2 angles you can find the third.

6. I did the law of sines but couldn't get an angle...

7. Originally Posted by BeSweeet
So what do I need to do? I've already found one angle, and I can't find the other two...
use the sine rule to find B,

$\frac{sin79.19}{8}=\frac{sinB}{3}$

rearrange to find B.

alternatively you can do 180-79.19-79.19

since triangle =180 degrees

where

A=79.19
B=21.61
C=79.19

8. Originally Posted by BeSweeet
I did the law of sines but couldn't get an angle...
I can't help fix your error without your work. Look at the setup:

sin79.19/8=sinA/8

Both sides have the exact same form and the same denominator. So they must have the same numerator meaning angle a=c.