Lesson 5

Read “Link the Ideas: The Cosine Law” on page 116 of the textbook. This section includes a proof of the cosine law for acute triangles. In the Going Beyond section of this lesson you will complete a proof of the cosine law for obtuse triangles.

 

Self-Check 1

 

Given the following triangle, state three different ways the cosine law can be written, depending on which angle you are working with. Answer

 

 

Example 1: The Obstacle Course

 

The cosine law can be used to solve the problem given in the Focus section.

 

 

Start by stating the correct cosine law for the question.

 

f 2 = d2 + e2 − 2de cos F

 

Remember that the angle in the equation is the angle across from the side you are trying to determine. In this example, ∠F is across from the side you are trying to determine.

 

f 2 = 252 + 302 − 2(25)(30) cos 40°

 

You might enter the equation above in more than one step. Remember that most calculators can deal with complicated expressions. Just enter the equation above, exactly as you see it. You will get this answer:

 

f 2 = 375.9333…

 

You must use the unrounded answer from your previous step. Many calculators let you do this using the ANS key, which stands for “answer from previous step.” For some calculators, you would enter Consult your calculator manual if you can’t find the ANS key on your calculator.

 

 

The unrounded value for f is 19.3890…. Round the final answer to one decimal place unless instructed otherwise.

 

f = 19.4 m

Read “Example 1: Determine a Distance” on page 116 of your textbook. Ensure that you are comfortable with the steps in this solution before moving on.

 

Self-Check 2

 

Complete questions 1.a., 1.c., 5.b., and 6.a. on pages 119 and 120 of the textbook. Answers