Law of sines - Trigonometric Ratios and Angle Measures
Law of sines
In this section, we will learn about the Law of Sines, also known as the Sines Rule. The Law of Sines is a formula that models the relationship between the sides and the angles of any triangle, be it a right-angled triangle, an obtuse triangle, or an acute triangle. In order to use the Law of Sines, we need to satisfy the "one pair, one additional information" condition (i.e. Angle-Angle-Side abbreviated as AAS, and Angle-Side-Angle abbreviated as ASA). We will also explore the concept of the Ambiguous Case of the Law of Sines.
Lessons
Notes:
Law of Sine
For any ABC,
and,
Use the Law of Sine when given a pair!
Ambiguous case
Ambiguous case of the Law of Sine arises when given SSA (side-side-angle)
Step 1) Use the given angle to find the height of the triangle:
Step 2) Check if,
< , then no triangles
, then 1 triangle
> , then 1 triangle
< < , then 2 triangles
Step 3) Solve the triangle(s)!
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1.
Given the following triangle ,
