1. Lesson 4

1.1. Discover

Mathematics 20-2 M1 Lesson 4

Module 1: Trigonometry

 
Discover
 

Sometimes it’s hard to choose which trigonometric formula to use. In the following activity you will consider what to look for when you need to choose a formula.

 

This picture shows an acute triangle with a 63 degree angle and a 49 degree angle. The side opposite the 63 degree angle is 10 cm, and the side opposite the 49 degree angle is labelled x.

Igor has decided that he can use the sine law to solve for length x:

 

 

 

Igor said he chose the sine law because it uses two sides and two angles. In order to solve an equation, there can be only one unknown quantity. For this triangle, three of the four needed values are known.

 

Igor is correct. Use the sine law when you know a side-angle pair (e.g., side a and ∠A) and another side or angle.

 

This picture shows an acute triangle with a 59 degree angle and a 52 degree angle. The side opposite the 59 degree angle is 8 cm, and the side opposite the unlabelled angle is labelled y.

 

For the next problem, Igor decides to use the sine law to solve for length y. He says, “In the previous diagram, I used the sine law because I knew three measurements in the triangle. I know three measurements for this second triangle, so I can also use the sine law for this problem.” Igor wrote the following equation:

 

 

 

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

Share 1
 

With a partner, complete the following:

  • Discuss whether Igor or Ronitra is correct, and justify your opinion.
  • Summarize your discussion.
  • Describe the conditions for using the sine law to solve a triangle problem.