Deriving the Law of Cosines

Multiple Choice

Which of the following is the law of sines?

• a² + b² = c²

• $$\sin x=\sin x\frac{1}{\sin x}$$  

• $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$  

• $$\tan A=\frac{\sin A}{\cos A}$$  

Multiple Choice

Which of the following given of triangle cannot be solved by law of sines?

I. One side and two angles are given.

II. Two sides and an angle opposite one of the sides given.

III. Two sides and an included angle are given.

IV. Three sides are given.

• I and II only

• II and III only

• III and IV only

• I, II and III only

Multiple Choice

What is the measure of angle A?

• 87°47′

• 77° 47′

• 68°12′

• 59° 47′

Law of Cosines

By Richard Mariano

There are four possible cases of problems involving the solution of oblique triangles.

​They are as follows:

Case 1: One side and two angles are given.

Case 2: Two sides and an angle opposite one of the sides are given.

​

Case 3: Two sides and an included angle are given.

Case 4: Three sides are given.

Law of Cosines​

Law of Cosines

Law of Cosines

Example 1. Finding Distance with the Law of Cosines

Law of Cosines

Example 2. Finding a Missing Angle with the Law of Cosines

Multiple Select

• a

• b

• c

• d

• e

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

A triangle has the lengths of its sides 32, 36, and 45 . What is the measure of the

angle opposite the side whose length is 32?

• $$35.48\degree$$  

• $$44.85\degree$$   

• $$52.51\degree$$  

• $$82.64\degree$$