Law of Sines ppt

Demonstration TeachingIn

Trigonometry

Right Triangle

Acute Triangle

Obtuse Triangle

TriangleSolved

three sides

three angles

Right Triangle

B B B B

a

Acute TriangleObtuse Triangle

Oblique Triangles

Oblique Triangle

is a triangle which does not contain a right angle.

How then do we solve oblique

triangles?

The Law of SinesIn any triangle ABC, the sides are proportional to

the sines of the opposite angles.

= = or reciprocal form

= =

Case II: Given two angles and the included side between them (ASA)

Case I: Given two angles and a side opposite one of them (AAS)

Case III: Given two sides and an angle opposite one of them Case IV: Given two sides and the included angle between them

Case v: Given three sides

Case I. Given two angles and a side opposite to one of them. (AAS)

Given: A = 48° C = 102° c = 25cm

Unknown : B , a, c

A

C

B

a=? b =?

c= 25 cm

48°

102°

?

Case I. Given two angles and a side opposite to one of them. (AAS)

Given: A = 63° C = 79° a= 12 in

Unknown : B , b, c

In ABC, A = 63°, B = 79°, and a = 12 in. Find ▲the length s of the other two sides and the measure of the third angle, C.

BA

C

a =12 inb =?

c= ?

63°

79°

?

Given: A = 75° C = 85° b = 10 cm

Unknown : B , a, c

Case II. Given two angles and the included side between them. (ASA)

A Bc = ?

b=10 cm a =?

C

85°

75° ?

Given: A = 59° C = 49° b = 13 cm

Unknown : B , a, c

Case II. Given two angles and the included side between them. (ASA)

A Bc = ?

b=13 cm a =?

C

59°

49°

?

is a triangle which does not contain a right angle.

Oblique Triangle

Law of SinesIn any triangle ABC, the sides are proportional to the

sines of the opposite angles. = = or reciprocal form

= =

Case I: Given two angles and a side opposite one of them (AAS)

Case II: Given two angles and the included side between them

(ASA)

Case III: Given two sides and an angle opposite one of

them

Assignment:

Answer Exercises 6.2 p. 167.