Lesson 4

1. Lesson 4

Mathematics 20-1 Module 2

Module 2: Trigonometry

Lesson 4: The Sine Law

Focus

This picture shows Khadija’s house, her shed, and the measurements she has made. The house is a square 10.7-metre wide, and there is a door at the upper-left corner. Immediately above the house is a triangle that shares a horizontal line with the back of the house. The bottom-right angle is 61 degrees, the bottom-left angle is unknown, and the upper angle is 40 degrees. The side across from the 61-degree angle is labelled d.

Khadija is building a walkway from her back door to her shed, which is located at the back of the yard. She needs to provide the length to a contractor in order to get a phone estimate for the cost of building the walkway. She knows her house is 10.7-m wide, and she has measured two angles as shown in the diagram.

How would you solve this problem to find the distance? In previous math courses, you solved triangle problems that involved right triangles—or triangles that had a 90° angle. But what about non-right triangles, as shown in this scenario?

There is a triangle in this problem, but it is not a right triangle. So, the primary trigonometric ratios cannot be used. In this lesson you will investigate the sine law, which can be used for oblique triangles.

Outcomes

At the end of this lesson you will be able to

use the sine law to solve for sides or angles in oblique triangles

determine how many solutions are possible in a situation called the ambiguous case with the sine law

Lesson Questions

You will investigate the following questions:

How can angles and sides in any triangle—oblique and right—be found?
How does your knowledge of solutions to equations of the form sin θ = k (from Lessons 1 and 2) affect solutions using the sine law?

Assessment

Your assessment may be based on a combination of the following tasks:

completion of the Lesson 4 Assignment (Download the Lesson 4 Assignment and save it in your course folder now.)
course folder submissions from Try This and Share activities
additions to Module 2 Glossary Terms and Formula Sheet