Law of Cosines basics

Which cases apply to the Law of Cosines?

• SAS

• SSS

• ASA

• AAS

• SSA

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

For Triangle ABC, which of the following applies?

• $\cos A=\frac{b^2-c^2+a^2}{2bc}$

• $\cos A=\frac{b^2+c^2-a^2}{2bc}$

• $\cos B=\frac{a^2+c^2-b^2}{2ac}$

• $\cos C=\frac{b^2+a^2-c^2}{2ba}$

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

For triangle ABC, which of the following applies

• $c^2=a^2+b^2-ab\cos C$

• $c^2=a^2+b^2-2ab\cos C$

• $a^2=c^2+b^2-cb\cos B$

• $b^2=a^2+c^2-2ac\cos B$

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Set up the law of cosines to find BC

• $a^2=30^2+21^2-\left(30\right)\left(21\right)\cos\left(123\right)$

• $a^2=30^2+21^2-2\left(30\right)\left(21\right)\cos\left(123\right)$

• $a^2=30^2+21^2-\left(30\right)\left(21\right)\sin\left(123\right)$

• $a^2=30^2+21^2-2\left(30\right)\left(21\right)\sin\left(123\right)$

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following statements are true about the triangle ABC?

• $a>b>c$

• $a>c>b$

• Angle C > Angle B

• Angle B > Angle C

Tags

CCSS.HSG.CO.C.10

Which of the following is the correct ratio to use to find angle A?

• $\cos A=\frac{10.4^2+18^2-21.9}{2\left(10.4\right)\left(18\right)}$

• $\cos A=\frac{21.9^2+18^2-10.4}{2\left(21.9\right)\left(18\right)}$

• $\cos A=\frac{21.9^2+10.4^2-18}{2\left(21.9\right)\left(10.4\right)}$

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following is the correct ratio to use to find angle B?

•  $\cos B=\frac{10.4^2+18^2-21.9}{2\left(10.4\right)\left(18\right)}$ 

•  $\cos B=\frac{21.9^2+18^2-10.4}{2\left(21.9\right)\left(18\right)}$ 

•  $\cos B=\frac{21.9^2+10.4^2-18}{2\left(21.9\right)\left(10.4\right)}$ 

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following is the correct ratio to use to find angle C?

•  $\cos C=\frac{10.4^2+18^2-21.9}{2\left(10.4\right)\left(18\right)}$ 

•  $\cos C=\frac{21.9^2+18^2-10.4}{2\left(21.9\right)\left(18\right)}$ 

•  $\cos C=\frac{21.9^2+10.4^2-18}{2\left(21.9\right)\left(10.4\right)}$ 

• none of these

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

 $\cos A=\frac{n}{d}$  mark the true statements about ratios

• A is undefined if  $\left|\frac{n}{d}\right|>1$  

• A is acute if  $0<\frac{n}{d}<1$  

• A is obtuse if  $-1<\frac{n}{d}<0$  

• A is right is  $\frac{n}{d}=1$  
  

Tags

CCSS.HSF.TF.A.2

While limited to two cases of triangles, the law of cosines is BETTER than the law of sines....

• because its solutions are easier to find

• only one solution is possible

• conceptually an extension of Pyth. Th.

• is a result of a triangle having three heights

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11