Introduction to the Cosine Rule for Finding Missing Lengths and Angles in Triangles

The video tutorial covers the use of trigonometry in solving problems involving triangles. It begins with an introduction to SohCahToa for right angle triangles and transitions to the cosine rule for non-right angle triangles. The cosine rule is explained in detail, including its derivation and application in finding missing side lengths and angles. The tutorial concludes with practical examples demonstrating how to apply the cosine rule in various scenarios.

Which trigonometric ratio is used to find the opposite side in a right-angle triangle?

• Secant

• Cosine

• Tangent

• Sine

What is required to apply the cosine rule to find a missing side?

• One side and one angle

• Two angles and a side

• Two sides and the included angle

• All three angles

In the derivation of the cosine rule, which theorem is used to calculate the height of the triangle?

• Area Formula

• Pythagoras' Theorem

• Sine Rule

• Law of Tangents

What is the formula for the cosine rule when finding a missing side?

• a^2 = b^2 + c^2 - 2bc cos A

• a^2 = b^2 + c^2 - 2bc sin A

• a^2 = b^2 + c^2 + 2bc cos A

• a^2 = b^2 - c^2 + 2bc cos A

When using the cosine rule to find an angle, what must you do with the formula?

• Multiply by 2

• Rearrange to solve for cos A

• Add all sides

• Subtract the smallest side

In the example given, what is the missing side length calculated using the cosine rule?

• 35 kilometers

• 68 kilometers

• 90 kilometers

• 83.46 kilometers

What is the angle found using the cosine rule in the example provided?

• 90 degrees

• 107.7 degrees

• 68 degrees

• 35 degrees