Law of Cosines - SAS

• Jan 21st 2013, 09:59 AM
alexthesauceboss
Law of Cosines - SAS
So, I am given SAS.

Now I must find the remaining angles and side.

I am given:

M<A=
M<B=20 degrees
M<C=
a=10mm
b=
c=15mm

and the triangle looks somewhat like this:

......10mm
B\---------|C
...\20........|
....\...........|
.....\..........|
......\.........|
.......\........|
........\.......|
15mm.\......|
..........\.....|
...........\....|
............\...|
.............\..|
...............A
• Jan 21st 2013, 12:10 PM
ebaines
Re: Law of Cosines - SAS
First use the law of cosines to find the length of b. Then use the law of sines to find the angle A, and finally angle C. Post back with what you get for answers and we'k check it for you.
• Jan 21st 2013, 12:32 PM
alexthesauceboss
Re: Law of Cosines - SAS
Quote:

Originally Posted by ebaines
First use the law of cosines to find the length of b. Then use the law of sines to find the angle A, and finally angle C. Post back with what you get for answers and we'k check it for you.

Ah! Well, b is ~ 4.85. Then, I did as you said with the law of sines to find that M<A is 44.85 degrees, and M<C is 115.15 degrees.

Is that correct?
• Jan 21st 2013, 12:41 PM
ebaines
Re: Law of Cosines - SAS
I get b = 6.56mm. Using the law of cosines:

$\displaystyle b^2 = a^2 + c^2 - 2ac \cos(b) = 10^2 + 15^2 - 2(10)(15)(0.9397) = 43.09$ , so b = 6.56