Trigonometry
posted by Laurianne .
Am I doing something wrong? I have to use the Law of Consines with the following numbers: a=30, b=15, c=17. I tried to find the angle a, since a is the longest side. Cos A=(15^2+17^230^2)/(2x17x15)=.7568 The inverse being 139 degrees. But when I multiply 15, the measure of b by sin 139/30, I get .32 or 18.66. This is 157. 180157=23 But when I multiply 17 by sine139/30 I get 21. Does this mean there are two triangles, or that I did it wrong?

a^2=b^2+c^22bcCosA
CosA= 1/2 * (b^2+c^2a^2)/bc
A= 139 deg, you are right on that.
Lets find angle B, by the law of sines
sinB/b=SinA/a or sinB= .3269 or B=19 deg
Lets find angle C by the law of sines
SinC/c=SinA/a or SinC=.3718 C=21.8 deg
check: do the sum of angles = 180 deg?
139+21.8+19=180 rounded.
All is well.