Is There a Straightforward Proof for the Cosine Rule?

In summary, the Cosine Rule, also known as the Law of Cosines, is a mathematical formula used to find the length of a side or measure of an angle in a triangle. It is derived from the Pythagorean theorem and is useful for solving non-right triangles. It is typically used in trigonometry and geometry. The main difference between the Cosine Rule and the Sine Rule is the use of cosine and sine, respectively. The Cosine Rule has many real-life applications, particularly in engineering, physics, and navigation.
  • #1
atwarwithmaths
6
0
Hi Guys/Girls,

I have a maths exam tomorrow and there is a chance I could be asked to prove the cosine rule or sine rule.

Well I have a simple proof of the sine rule but cannot find a simple one for the cosine. They all seem very advanced.

Would anybody have a straightforward proof for the cosine rule?

Thanks,
atwarwithmaths
 
Mathematics news on Phys.org
  • #3
Thats perfect thanks.. Stupid me, I turn to wikipedia for everything else.!
 

1. What is the Cosine Rule?

The Cosine Rule, also known as the Law of Cosines, is a mathematical formula used to find the length of a side or measure of an angle in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles.

2. How is the Cosine Rule derived?

The Cosine Rule is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. By rearranging this equation and substituting in the cosine of one of the angles, the Cosine Rule can be derived.

3. When should the Cosine Rule be used?

The Cosine Rule is useful when solving non-right triangles, as it can be used to find the length of a side or measure of an angle that is not directly opposite a right angle. It is commonly used in trigonometry and geometry to solve problems involving triangles.

4. What is the difference between the Cosine Rule and the Sine Rule?

The Cosine Rule and the Sine Rule are both used to solve problems involving triangles. The main difference is that the Cosine Rule involves the cosine of an angle, while the Sine Rule involves the sine of an angle. The Cosine Rule is typically used to find the length of a side or measure of an angle, while the Sine Rule is used to find the length of a side or measure of an angle when a ratio of two sides and an angle opposite one of those sides is known.

5. Are there any real-life applications of the Cosine Rule?

Yes, the Cosine Rule has many real-life applications, particularly in fields such as engineering, physics, and navigation. It can be used to calculate distances between objects, determine the trajectory of a projectile, and even measure the height of a building or mountain.

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