List the angels of triangle bcd from smallest to largest?

1. BC=7, CD=12, BD=16

2. BC=6.1, CD=5.2, BD=6.3

3. BC=22, CD=24, BD=13

2. Think about a triangle with whatever sides you choose. The bigger the side the larger the angle opposite of it is. So, for the first one,

angle A, angle B, angle D
each side corresponds to the angle opposite or the angle with the letter the side is missing.

3. ## This comes

from the law of sines since $\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}$ since as x tends toward 0, $sin(x)$ tends towards 0

4. Originally Posted by Mathstud28
from the law of sines since $\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}$ since as x tends toward 0, $sin(x)$ tends towards 0
i think we need to start off with the law of cosines. we need at least one angle to use the law of sines

5. ## O yeah

I know that I was just trying to explain that the reason the larger the opposite angle the larger the side is that the smaller than angle the smaller $sin(\theta)$ which is in the denominator so it makes the ratio bigger...or am I off...I've never seen this before and I just had a brain storm...haha probably should have thought it through better

6. Originally Posted by Mathstud28
I know that I was just trying to explain that the reason the larger the opposite angle the larger the side is that the smaller than angle the smaller $sin(\theta)$ which is in the denominator so it makes the ratio bigger...or am I off...I've never seen this before and I just had a brain storm...haha probably should have thought it through better
well, that discussion is all well and good. but i am afraid it's unnecessary. if the poster just finds two angles, he/she can get the third by subtracting the sum of the previous two from 180, and then, after knowing the value of the angles, there will be no question as to which is largest or smallest. worrying about that from the get-go is slowing yourself down. just find the angles, you have to find them anyway