Law of Cosines and Triangle Properties

This video tutorial explains how to find angle measures in oblique triangles using the law of cosines. It reviews methods for solving triangles, including the Pythagorean theorem and trigonometric laws. The law of cosines is introduced, showing its formula and application in two cases: finding an angle when all sides are known, and finding a side when two sides and an included angle are known. The tutorial concludes with a caution on the correct application of trigonometric laws.

What is the primary focus of this lesson?

• Solving right triangles using the Pythagorean theorem

• Understanding the Law of Sines

• Solving oblique triangles using the Law of Cosines

• Learning about trigonometric inverses

Which formula is used to find the relationship between the sides and an angle in a triangle?

• Law of Cosines

• Law of Sines

• Pythagorean theorem

• Trigonometric inverses

When using the Law of Cosines, what does the lowercase 'c' represent?

• The sum of all sides

• The hypotenuse of the triangle

• The side opposite angle C

• The angle opposite side c

What is the sum of all interior angles in any triangle?

• 90 degrees

• 360 degrees

• 180 degrees

• 270 degrees

In the first case of the Law of Cosines, what is required to find an angle?

• Two angles and one side

• All three sides

• One angle and two sides

• All three angles

What is the approximate measure of angle Y when using the Law of Cosines with sides 14, 10, and 21?

• 45.2 degrees

• 90.0 degrees

• 34.8 degrees

• 60.0 degrees

In the second case of the Law of Cosines, what is known to find the missing side?

• Two sides and the included angle

• All three sides

• All three angles

• One side and two angles

What is the approximate length of side MN when angle P is 81 degrees and the other sides are 11 and 8?

• 12.55 units

• 9.8 units

• 15.0 units

• 10.5 units

What should you be cautious about when using trigonometric laws?

• Using trigonometric inverses for all calculations

• Using the Law of Cosines for right triangles

• Using the Law of Sines for all triangles

• Using the correct trigonometric law for each case

Which trigonometric law is not suitable for every triangle case?

• Pythagorean theorem

• Law of Cosines

• Both Law of Sines and Law of Cosines

• Law of Sines