Law of Sines

Concept

Definition of law of sines :

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

diagram showing the ratios for law of sines

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 ;

formula for 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,

solution for the question on law of sines

Related Topic :Learn the law of cosines.

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