## Reflection: Grappling with Complexity Law of Sines Introduction - Section 2: Discovering Law of Sines

As students worked through the Law of Sines activity one student really got stuck when he had 2 expressions equivalent to k in question 6.  He questioned how they could be equal since they were not the same angle and the same side. I began going back over his process and he made the comment that shows a deeper understanding of the ratio than I expected.

He noticed that in the diagram angle C is larger than angle A which means that side c is larger than side a. In the equation you are taking a smaller side times the sine of a larger angle and a larger side time the sine of a smaller angle so these k=a sin C and k=c sin A so a sin C= c sin A makes sense.

At first I had to think about the students reasoning but the students is understanding the the larger the angle the larger the value of sine when you have an acute angle. For this student making this relationship helped him with what he had determined using right triangles.

Grappling with Complexity: Student reasoning

# Law of Sines Introduction

Unit 6: Solving Problems Involving Triangles
Lesson 3 of 13

## Big Idea: Students prove the Law of Sines through a discovery activity.

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Standards:
Subject(s):
Math, Trigonometry, triangles (Determining Measurements), law of sines, triangle measurement, problem solving
45 minutes

### Katharine Sparks

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