Precalculus: Law of Sines

Objectives

• Students will understand how the Law of Sines is derived.
• Students will understand when the Law of Sines can be used to find missing sides and angles in a triangle.
• Students will be able to solve for missing sides and angles in a triangle using the Law of Sines, when appropriate.

Vocabulary

• sine of an angle
• obtuse angle
• acute angle
• right angle
• Ambiguous Case of the Law of Sines

About the Lesson

This lesson involves exploring the relationship known as the Law of Sines.
As a result, students will:

• Manipulate a triangle to observe the equality of ratios of side lengths and sines of opposite angles.
• Manipulate a triangle to decide when the Law of Sines gives an unambiguous result.
• Consider the Law of Sines in connection with previous knowledge about right triangle trigonometry.
• Determine when the Law of Sines can be used to solve for unknown side lengths and angle measures in a triangle, and apply it to solve when possible.