side opposite given angle - st. johns county school district · pclesson 6.1(b)_notes.notebook...

PC­­Lesson 6.1(b)_notes.notebook December 02, 2015

6.1(b) Law of Sines

Students will be able to . . .

• use the Law of Sines to solve oblique triangles (AAS, ASA, or SSA).

• find areas of oblique triangles and use the Law of Sines to model and solve real­life problems.

If two sides and one opposite angle are given, then three possible situations can occur: (1) no such triangle exists, (2) one such triangle exists, or (3) two distinct triangles satisfy the conditions.

Given angle

non­opposite side

h

side opposite given angle

PC­­Lesson 6.1(b)_notes.notebook December 02, 2015

h

A

b

Given : Angle (A), side (a), side (b)

Determine how many triangles can be made with each of the lengths of a.

a1a2 a4 a5

a3

PC­­Lesson 6.1(b)_notes.notebook December 02, 2015

a < h no triangle formed

a = h 1 triangle formed (right triangle)

a = b 1 triangle formed (isosceles)

A

bh

a

B

h < a < b 2 triangles formed

A

b

B2A

b

B1

A

b

B2A

b

B1

A

bh

a

A

b ha

B

a > b one triangle formed

A

bh

a

h = b sin A

PC­­Lesson 6.1(b)_notes.notebook December 02, 2015

Examples

Use the Law of Sines to solve the triangle. If two solutions exist, find both.

(a) A = 58o, a = 4.5, b = 12.8

(b) A = 78o, a = 207, c = 210