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Lesson 3

1. Lesson 3

1.1. Discover

Mathematics 20-2 M1 Lesson 3

Module 1: Trigonometry

 
Discover
 

In the previous lesson you learned that the sine law can be used for any triangle, including oblique and right triangles. Although it is true that the sine law can be applied to any triangle, sometimes the information that you are given is not enough to use the sine law.

 

Consider Jennifer and David’s problem. They have not been given enough information to conclude that their triangle is a right triangle, so they know that they can’t use the primary trigonometric ratios or the Pythagorean theorem. In their math class, they learned that the sine law can be used for any triangle, but they are not sure that they have enough information to use the sine law.

 

Share 1
 

Consider the triangle that David and Jennifer created to help them find the length of the rope they need to purchase.

 

This is a picture of an oblique triangle with vertices D, E, and F. Angle F has a measure of 40 degrees, side d has a length of 25 m, and side e has a length of 30 m. Side f is the unknown to be calculated.

 

With a partner, write out all three equations of the sine law. Why can’t the sine law be used to find the length of side f?

 

m20_2_tipbar_2.jpg

Recall that the sine law is a compact way of writing the following three equations:







Share 2
 

Watch the animation titled Jennifer and David’s Solution to see a method for solving the problem.

 

 

This is a screenshot for Jennifer and David’s Solution.

 

With a partner, decide what would change if the triangle in Jennifer and David’s problem had the following measurements:

  • d = 45 m
  • e = 54 m
  • ∠F = 57°

You may want to replay the animation.