CK-12-Pre-Calculus Concepts

4.5. Law of Cosines http://www.ck12.org

Guided Practice

1. Determine the length of sider.


2. Determine the measure of angleTin degrees.


3. Determine the measure of angleSin radians.
   Answers:
   1.r^2 = 362 + 422 − 2 · 36 · 42 ·cos 63
   r= 41. 07 ...


4. 36^2 = ( 41. 07 ...)^2 + 422 − 2 ·( 41. 07 ...)· 42 ·cosT
   T≈ 51. 34 ...◦


5. You could repeat the process from the previous question, or use the knowledge that the three angles in a triangle
   add up to 180.

63 + 51. 34 ...+S= 180

S≈ 65. 65 ◦· 180 π◦≈ 1. 145 ...radians

Practice

For all problems, find angles in degrees rounded to one decimal place.
In∆ABC,a= 12 ,b= 15 ,andc=20.

1. Find the measure of angleA.


2. Find the measure of angleB.


3. Find the measure of angleC.


4. Find the measure of angleCin a different way.
   In∆DEF,d= 20 ,e= 10 ,andf=16.


5. Find the measure of angleD.


6. Find the measure of angleE.


7. Find the measure of angleF.
   In∆GHI,g= 19 ,^6 H= 55 ◦,andi=12.