Lesson 3

1. Complete “Check Your Understanding” question 2 on page 151 of your textbook. Answer
   
   
2. Complete “Practising” questions 4 and 11 on pages 151 and 152 of your textbook. Answer

The cosine law can also be used to determine angle measures. Because the formula includes one angle, if you are given all three sides, the cosine law can be used to solve for any angle in a triangle.

Read “Emilie’s Solution: Rearranging the cosine law before subtracting” on page 148 of your textbook to see how Emilie rearranges the cosine law formula to isolate cos B. This will make it much easier to find an angle when given all three side lengths.

The rearranged form is

You know that the cosine law can be written in three ways, depending on which side you are looking for:

• a2 = b2 + c2 − 2bc cos A
• b2 = a2 + c2 − 2ac cos B
• c2 = a2 + b2 − 2ab cos C

The same is true when the formula is rearranged to solve for the cosine of an angle.