Table of Contents
Introduction to the Law of Sines
The law of sines is a mathematical statement that relates the angles of a triangle to the lengths of its sides. The law states that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. This relationship can be used to solve for any angle or side in a triangle.
Define Law of Sines
The law of sines states that the ratio of the length of the opposite side to the length of the hypotenuse is the same for all three sides of a triangle.
Sine Rule Proof
The sine rule states that the sine of an angle is equal to the sine of its adjacent angle multiplied by the cosine of the angle between them.
Proof:
Let A be an angle and let B be its adjacent angle. Let C be the angle between A and B.
We will show that:
sin A = sin B × cos C
We can use the Pythagorean theorem to show that:
cos C = (length of BC)² – (length of AC)²
Now, we can substitute this into the equation to get:
sin A = sin B × (length of BC)²/(length of AC)²
sin A = sin B × (cos C)
The Formula For Sine Rule
The sine rule states that the sine of an angle is equal to the sine of its opposite side divided by the length of the opposite side.
