Law of Sines and Cosines Formula - Understanding the Sine and Cosine Rules

The Law of Sines and Cosines, also known as the Sine and Cosine rules, serve as essential tools in solving oblique triangles - triangles that don't have a right angle. These triangles can either have all angles acute or just one angle as obtuse.

Sine Rule Explained

There are two specific cases in which we apply the Sine Rule:

Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA)
Side-Side-Angle (SSA)

According to the Sine Rule, the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. In other words:

a/ Sin A = b / Sin B = c / Sin C

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Cosine Rule Simplified

The Cosine Rule states that the square of the length of any side of a triangle is equal to the sum of the squares of the lengths of the other two sides, minus twice their product multiplied by the cosine of the angle between them.

a^2 = b^2 + c^2 – 2bc cos A , cos A = (b^2 + c^2 – a^2) / 2bc
b^2 = a^2 + c^2 – 2ac cos B , cos B = (a^2 + c^2 – b^2) / 2ac
c^2 = a^2 + b^2 – 2ab cos C , cos C = (a^2 + b^2 – c^2) / 2ab

For more information on trigonometric concepts and formulas, continue browsing our website.

Frequently Asked Questions

What is the law of Sine and Cosine?

The law of Sine and Cosine also called Sine and Cosine rules are used for finding the solution for the oblique triangle. It is a triangle which is not a right triangle.

When do we use the Sine Rule?

There are two cases where we use the Sine Rule: AAS or ASA and SSA.

What does the law of Cosine state?

The law of Cosine states that the square of the given length of the side of a triangle is equal to the sum of the squares of the length of other sides minus twice their product and multiplied by the cosine of their included angle.