- Home
- Precalculus
- Trigonometry
Law of sines
- Intro Lesson12:58
- Lesson: 1a4:10
- Lesson: 1b4:01
- Lesson: 24:28
- Lesson: 315:18
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 = ho ), Use cosine ratio to calculate angles and sides (Cos = ha ), Use tangent ratio to calculate angles and sides (Tan = ao )
Related Concepts: Quotient identities and reciprocal identities, Pythagorean identities, Sum and difference identities
Lessons
Law of Sine
For any △ ABC,
sin(A)a =sin(B)b =sin(C)c
and,
asin(A) =bsin(B) =csin(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=bsin(A)
Step 2) Check if,
Sidea < h, then no triangles
Sidea=h, then 1 triangle
Sidea > h, then 1 triangle
h < Sidea < Sideb, then 2 triangles
Step 3) Solve the triangle(s)!
For any △ ABC,
sin(A)a =sin(B)b =sin(C)c
and,
asin(A) =bsin(B) =csin(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=bsin(A)
Step 2) Check if,
Sidea < h, then no triangles
Sidea=h, then 1 triangle
Sidea > h, then 1 triangle
h < Sidea < Sideb, then 2 triangles
Step 3) Solve the triangle(s)!
- Introduction
- 1.Given the following triangle △ABC,
a)Solve for∠Cb)Solve for a - 2.Solve for side x
- 3.Ambiguous case: SSA triangles
In △DEF, DE=21cm, ∠F=45°, and EF=24cm; find DF.
Do better in math today
10.
Trigonometry
10.1
Converting between degrees and radians
10.2
Radian measure and arc length
10.3
Angle in standard position
10.4
Coterminal angles
10.5
Reference angle
10.6
Find the exact value of trigonometric ratios
10.7
ASTC rule in trigonometry (All Students Take Calculus)
10.8
Unit circle
10.9
Trigonometric ratios for angles in radians
10.10
Solving first degree trigonometric equations
10.11
Determining non-permissible values for trig expressions
10.12
Use sine ratio to calculate angles and side (Sin = ho )
10.13
Use cosine ratio to calculate angles and side (Cos = ha )
10.14
Use tangent ratio to calculate angles and side (Tan = ao )
10.15
Combination of SohCahToa questions
10.16
Law of sines
10.17
Law of cosines
10.18
Sine graph: y = sin x
10.19
Cosine graph: y = cos x
10.20
Tangent graph: y = tan x
10.21
Cotangent graph: y = cot x
10.22
Secant graph: y = sec x
10.23
Cosecant graph: y = csc x
10.24
Graphing transformations of trigonometric functions
10.25
Determining trigonometric functions given their graphs
10.26
Quotient identities and reciprocal identities
10.27
Pythagorean identities
10.28
Sum and difference identities
10.29
Double-angle identities
10.30
Word problems relating ladder in trigonometry
10.31
Word problems relating guy wire in trigonometry
10.32
Other word problems relating angles in trigonometry