Law of sines

Intro Lesson
12:58
Lesson: 1a
4:10
Lesson: 1b
4:01
Lesson: 2
4:28
Lesson: 3
15:18

Learn

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.

Basic concepts: Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

), Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

), Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

Lessons

Law of Sine
For any

\triangle

ABC,

\frac{a}{\sin(A)}

=\frac{b}{\sin(B)}

=\frac{c}{\sin(C)}

and,

\frac{\sin(A)}{a}

=\frac{\sin(B)}{b}

=\frac{\sin(C)}{c}

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:

h=b \sin (A)

Step 2) Check if,

Side\;a

h

then no triangles

Side\;a=h

then 1 triangle

Side\;a

h

then 1 triangle

h

Side\;a

Side\;b

then 2 triangles

Step 3) Solve the triangle(s)!

Introduction

1.
Given the following triangle $\triangle ABC$ ,

a)
Solve for $\angle C$

b)
Solve for $a$

2.
Solve for side $x$

3.
Ambiguous case: SSA triangles
In $\triangle DEF$ , $DE=21cm$ , $\angle$ $F=45$ °, and $EF=24cm$ ; find $DF$ .

Law of sines

Law of sines

Lessons

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