6.1 Laws of Sines

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

The Laws of Sines

Using the Law of Sines Given: How do you find angle B?

Using the Law of Sines Given: How do you find side b?

Using the Law of Sines Given: How do you find side b?

Using the Law of Sines Given: How do you find side b?

Using the Law of Sines Given: How do you find side c?

Using the Law of Sines Given: How do you find side c?

The Ambiguous Case Look at this triangle. If we look at where angle A Is Acute

The Ambiguous Case Look at this triangle. If we look at If a = h, then there is one triangle

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

The Ambiguous Case Look at this triangle. If we look at If a > b, then there is one triangle

The Ambiguous Case Look at this triangle. If we look at If h< a <b, then there is two triangles

The Ambiguous Case Do you remember the Hinge Theorem from Geometry. Given two sides and one angle, two different triangles can be made.

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

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

Area of an Oblique triangle Using two sides and an Angle.

Find the missing Angles and Sides Given:

Find the missing Angles and Sides Given:

Find the missing Angles and Sides Given:

Homework Page 416 #1, 7, 13, 19, 25, 31, 37, 25, 31, 37, 43, 49 43, 49

Homework Page 416 #4, 10, 16, 22, 28, 34, 40, 46, 52