Law of Sines
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
= 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 ;
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.
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