Lesson 4

Discover

 

The math in this lesson relies on a standard way of labelling triangles:

• Sides are named with lowercase letters.
  
  
• Angles are named with uppercase letters.

Sides and their opposite angles are named with the same letter (for example, side b and ∠B are opposite each other). The animation How to Label a Triangle shows this naming convention in more detail.

Watch Khadija’s Solution to see a way to create and use right triangles to solve Khadija’s problem.

Share 1

 

With a partner, discuss and try to agree on the answers to the following questions. The goal of Share 1 is to get you thinking; don’t worry if you can’t answer all the questions.

 

At the end of the animation, Khadija concludes with the equation

1. What, if anything, would change if Khadija’s triangle had the measurements a = 6, ∠A = 52°, and ∠D = 53°?
   
   
2. What, if anything, would change if Khadija’s triangle had the measurements a = 15.2, ∠A = 63°, and ∠D = 46°?
   
   
3. Is there any conclusion you can draw from your answers to questions 1 and 2? Explain.

Try This 1

Khadija concluded with an equation involving ratios of sines: The applet Sine Law Explorer also shows ratios involving sines. In Sine Law Explorer, drag the points of the triangle to change the measure of the angles and lengths of sides. Observe what happens to the ratios.

Share 2

 

Compare your observations with a partner. With your partner, describe an equation or relationship that appears to be true for all triangles.

 

Place a copy of your conclusion in your course folder. Your teacher may ask to see your conclusion later.