# Law of Sines

Concept

Definition of *law of sines* :

Let us find out how the law of sines is derived.

We drop a perpendicular from A to the base of the triangle. Regardless of whether the angle in question is acute or obtuse, the steps for proving the law of sines remain the same.

Let h denote the height of the triangle.

When the angle B is acute, sine B = . However, this also holds true when angle B

is obtuse in the 2 nd quadrant. With the use of supplementary angles, we can deduce

that sine
= sine . This means that sine ABC is equivalent to sine ABD.

Similarly, whether angle C is acute or obtuse, sine c = .

This brings us to the conclusion that h is equal to both b sine c and c sine b.

From this equation, we arrive at the law of sines ;

Examples

Apply the law of sines into the following examples

A triangle ABC has sides AB = 2 , BC = 1. Angle C is
45 . Find angle A.

It would be a good idea to draw the triangle out before attempting any questions on the law of sines

Subsituiting in the law of sines,

Related Topic :Learn the law of cosines.

Return to Trigonometry Help or Basic Trigonometry .