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+17^2-30^2)/(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. 180-157=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?

Question

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+17^2-30^2)/(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. 180-157=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?

Answer 1

a^2=b^2+c^2-2bcCosA

CosA= 1/2 * (b^2+c^2-a^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.