James B. answered • 06/02/16

Experienced, Patient, Passionate Trigonometry Tutor

Since you have the measures for all the sides, You would use the law of cosines to find any 1 of the 3 angles.

Note that in the typical diagram, the angles are named using upper case letters, and the sides opposite those angles will have lower case letters.

let a = 142, b = 185, c = 211

Law of Cosines: 1 of 3 formulas

c

^{2}= a^{2}+ b^{2}- 2ab (Cos C)Plug in the side measures ... then solve for Cos C

211

^{2}= 142^{2}+ 185^{2}- 2(142)(185)(Cos C)44,521 = 20,164 + 34,225 -52,540(Cos C)

44,521 = 54,389 - 52,540(Cos C)

Subtract 54,389 from both sides

-9,868 = -522,540(Cos C)

Divide both sides by -522,540

,01888468 = Cos C

Use the inverse trig function (in degree mode) to find the measure of angle A

Cos

^{-1}.01888468 = 88.92 degrees*** Angle C is 88.92 degrees

Now use the law of sines to find a second angle

(Sine C)/c = (Sine B)/b

(Sine 88.92)/211 = (Sine B)/185

Solve for the Sine B by multiplying both sides by 185

185(.99982235)/211 = Sine B

.8766214917 = Sine B

Use inverse Sine function (in degree mode) to find the measure of angle A

sine (.8766214817) = A

*** Angle A = 61.24

Since we have 2 of the angles, we subtract their sum from 180 to get the third angle ... The sum of the internal angles of all triangles is 180 degrees

Angle B = 180 - (61.24 + 88.92)

*** Angle B = 29.84