Cosine Rule and Triangle Properties

The video tutorial begins with an introduction to Pythagoras' theorem, explaining its application to right angle triangles. It then explores how triangles can be modified to have non-right angles and introduces the cosine rule as a solution for calculating side lengths in such cases. The cosine rule is explained in detail, showing how it adjusts Pythagoras' theorem to accommodate different angles, including obtuse angles. The tutorial concludes with practical applications of the cosine rule, demonstrating its versatility in solving various triangle problems.

What is the primary limitation of the Pythagorean theorem?

• It only applies to equilateral triangles.

• It only applies to right-angle triangles.

• It only applies to isosceles triangles.

• It only applies to scalene triangles.

When modifying a right-angle triangle to have an acute angle, what happens to the length of side c?

• It becomes equal to side a.

• It remains the same.

• It becomes shorter.

• It becomes longer.

What is the purpose of the cosine rule in relation to the Pythagorean theorem?

• To find the perimeter of a triangle.

• To calculate the area of a triangle.

• To apply the Pythagorean theorem to non-right-angle triangles.

• To simplify calculations for right-angle triangles.

How does the cosine rule adjust the Pythagorean theorem for non-right-angle triangles?

• By adding a term involving sine.

• By dividing by the hypotenuse.

• By multiplying by a constant factor.

• By subtracting a term involving cosine.

What happens to the value of cos(θ) when θ is an obtuse angle?

• It remains unchanged.

• It becomes zero.

• It becomes negative.

• It becomes positive.

In the cosine rule, what does the term -2ab cos(C) represent?

• The adjustment for right angles.

• The adjustment for obtuse angles.

• The adjustment for acute angles.

• The adjustment for all angles.

What is the result of cos(90 degrees) in the context of the cosine rule?

• 0

• 1

• -1

• Undefined

How does the cosine rule ensure accuracy for all triangle types?

• By focusing on right angles only.

• By ignoring obtuse angles.

• By adjusting for angle size.

• By using only positive values.

What is the significance of the lowercase 'c' in the cosine rule equation?

• It represents the area.

• It represents an angle.

• It represents the hypotenuse.

• It represents a side length.

What is the main advantage of the cosine rule over the Pythagorean theorem?

• It only uses whole numbers.

• It requires fewer calculations.

• It applies to all triangles.

• It is simpler to use.