# 6.1 Laws of Sines - Ms. Milton

Laws of Sines The Laws of Sine can be used with Oblique triangle Oblique triangle is a triangle that contains no right angle. B a c C

b A The Laws of Sines Or B a b

c sin A sin B sin C a c C b A

Example 1 You are given a triangle, ABC, with angle A = 70, angle B = 80 and side a = 12 cm. Find the measures of angle C and sides b and c. B 80 a = 12 c

A 70 b C Using the Law of Sines Given: C mA 102.4 mC 16.7

mB b a 21.6 b c a A c

B The Ambiguous Case Look at this triangle. If we look at where angle A Is Acute h b sin A A C

b a h B The Ambiguous Case Look at this triangle. If we look at

C b h b sin A A If a = h, then there is one triangle ha B

The Ambiguous Case Look at this triangle. If we look at C b h b sin A A If a < h, then there is no triangle

a h B The Ambiguous Case Look at this triangle. If we look at C b

h b sin A A If a > b, then there is one triangle a h B

The Ambiguous Case Look at this triangle. If we look at C b h b sin A A a

h B' If h< a

triangles can be made. 15 42 11 15 42 11 http://mrself.weebly.com/5-5-the-hinge-theorem.html

The Ambiguous Case Where Angle A is Obtuse. If a b, there is no triangle a b A

The Ambiguous Case Where Angle A is Obtuse. If a > b, there is one triangle a b A Area of an Oblique triangle

Using two sides and an Angle. 1 Area bc SinA 2 1 Area ab SinC 2 1 Area ac SinB 2 Find the missing Angles and Sides

Given: A 36 , a 8 , b 5 Find the missing Angles and Sides Given: A 36 , B 21.5 , C 122.5 a 8 , b 5 36 21.5 C 180 C 122.5 Find the missing Angles and Sides Given:

A 36 , B 21.5 , C 122.5 a 8 , b 5 c 8 Sin122.5 Sin36 8 Sin122.5 c Sin36 c 11 .48

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