Lesson 6.2 Law of Cosines Essential Question: How do you use trigonometry to solve and find the areas of oblique triangles?

What is an oblique triangle? A triangle that has no right angles

To use Law of Sines we needed one side and its opposite angle To use Law of Sines we needed one side and its opposite angle. When you are given three sides (SSS) or two sides and their included angle (SAS), none of the ratios in the Law of Sines would be complete. You would need to use the Law of Cosines.

What is the Law of Cosines? It’s the relationship between the sides and angles of non-right triangles. This is used to find angles of a general triangle.

Law of Cosines 𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑏𝑐 cos 𝐴 𝑏 2 = 𝑎 2 + 𝑐 2 −2𝑎𝑐 cos 𝐵 𝑐 2 = 𝑎 2 + 𝑏 2 −2𝑎𝑏 cos 𝐶

Alternative Form of Law of Cosines cos 𝐴 = 𝑏 2 + 𝑐 2 − 𝑎 2 2𝑏𝑐 cos 𝐵 = 𝑎 2 + 𝑐 2 − 𝑏 2 2𝑎𝑐 cos 𝐶 = 𝑎 2 + 𝑏 2 − 𝑐 2 2𝑎𝑏

How do you solve an oblique triangle? If given information about the three sides, or two sides and their included angle, use the Law of Cosines.

Find the angles in the given triangle.

Find the angles in the given triangle.

Find the angles in the given triangle.

Find the remaining angles and side of the triangle.

Find the remaining angles and side of the triangle.

The pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. (The pitcher’s mound is not halfway between home plate and second base.) How far is the pitcher’s mound from first base?

How do you use trigonometry to find the area of an oblique triangle? Use Heron’s Formula

Heron’s Formula 𝐴𝑟𝑒𝑎= 𝑠 𝑠−𝑎 𝑠−𝑏 𝑠−𝑐 where 𝑠= 𝑎+𝑏+𝑐 2

Find the area of the triangle.

Find the area of the triangle.

Find the area of the triangle.

How do you use trigonometry to solve and find the areas of oblique triangles?

Ticket Out the Door Find the missing measures of the triangle.