Lesson 4

1. Lesson 4

1.2. Discover 2

Mathematics 20-2 M1 Lesson 4

Module 1: Trigonometry

This picture shows an oblique triangle with sides of lengths 11 cm, 21 cm, and x. The angle between the 11 cm and 21 cm sides is 73 degrees.

To solve for the length of x in the following triangle, Igor wrote the following equation:

x2 = 212 + 112 − 2(21)(11) cos 73°

Igor said this is valid because the cosine law has three sides and an angle, and, in order to use an equation, you must know all but one of these quantities. Three quantities are known in the triangle.

This picture shows an oblique triangle with sides of lengths 6 cm, 8 cm, and y. The angle opposite the 8 cm side is 76 degrees.

Igor has decided to also use the cosine law to solve for length y. He says, “In the previous problem, I used the cosine law because I knew three of the four quantities in the equation. I know three of the four quantities in this problem, so I can also use the cosine law here as well.” Igor wrote the following equation:

y2 = 82 + 62 − 2(8)(6) cos 76°

Ronitra says that Igor is not using the cosine law correctly.

Share 2

With a partner, complete the following:

Discuss whether Igor or Ronitra is correct.
Summarize your discussion.
Describe the conditions for using the cosine law to solve a triangle problem.