# Law of Sines

From NCTM "Illuminations".  Detailed lesson plan with student activity sheets. Students use right triangle geometry to develop the Law of Sines.  Includes options for assessment.  The ambiguous case is addressed in the "Extensions" section at the end of the lesson.  Would be nicely paired with the following interactive demo in GeoGebra:  http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/LawOfS....  Students learn the law of sines, then use it to find missing side and angles. Lesson includes ambiguous case.

### Standards & Objectives

CLE 3103.4.4
Know and use the Law of Sines to find missing sides and angles of a triangle, including the ambiguous case.
CLE 3108.4.10
Develop the tools of right triangle trigonometry in the contextual applications, including the Pythagorean Theorem, Law of Sines and Law of Cosines.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.

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Learning objectives:

Students will:

• Use right triangle trigonometry to develop the law of sines.
• Use the law of sines to solve problems.
Essential and guiding questions:
• Given: ΔABC with m∠A = 79.39°, m∠B = 44.77°, and a = 7.07 cm. Is there a unique triangle with the following angle and side measures? Why?
• If two angles and a non‑included side of a triangle are known, the law of sines can be used to determine the missing angle and sides. For what other combinations of angles and sides could the law of sines be used to determine the missing angles and sides of a triangle?
• Of ASA and SSA, which guarantees a unique triangle? Why?

### Lesson Variations

Blooms taxonomy level:
Applying
Extension suggestions:

An extension to this lesson is included in the material in the link.