Is the Pythagorean theorem a special case of the law of cosines?

The Pythagorean Theorem is a special case of the law of cosines, a2 + b2 – 2*a*b*cos (theta) = c2 because cos (theta) = 0 when the angle is a 90 degree or right angle. We also learned that the converse of the Pythagorean Theorem is true as well.

What is the general rule for Pythagoras Theorem?

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Why is the Pythagorean theorem only a theorem?

It is not. It is a statement about the relationship between the lengths of the sides of a mathematical concept known as a right triangle. And the Pythagorean theorem is a mathematical theorem, not a scientific hypothesis.

Which came first Pythagorean theorem or Law of Cosines?

Which Came First: The Pythagorean Theorem or the Law of Cosines? The Pythagorean Theorem clearly came before the Law of Cosine. The variation of the theorem is used within the Law of Cosine.

How Pythagorean theorem changed the world?

The Pythagoras’ theorem has changed. For the past 2500 years, the Pythagoras’ theorem, arguably the most well-known theorem in the world, has greatly helped mankind to evolve. Its useful right angles are everywhere, whether it is a building, a table, a graph with axes, or the atomic structure of a crystal.

Which of the following conditions is applicable for law of cosines?

Thus, the law of cosines is valid when C is an obtuse angle. Case 2. Now consider the case when the angle at C is right. The cosine of a right angle is 0, so the law of cosines, c2 = a2 + b2 – 2ab cos C, simplifies to becomes the Pythagorean identity, c2 = a2 + b2, for right triangles which we know is valid.

Where does the cosine rule come from?

a2 = b2 + c2 – 2bc cos 90º. a2 = b2 + c2 – 2bc cos 90º = b2 + c2 – 2bc × 0 = b2 + c2. And this gives us exactly what Pythagoras’ Theorem gives us because a is the side opposite the right angle – it is the hypotenuse of the triangle. So the Cosine Rule is a generalisation of Pythagoras’ Theorem.

What is the relationship between the cosine rule and the Pythagorean Theorem?

The Law of Cosines states: c2=a2+b2−2ab cosC . This resembles the Pythagorean Theorem except for the third term and if C is a right angle the third term equals 0 because the cosine of 90° is 0 and we get the Pythagorean Theorem.