Law of Sines
Lesson · Beginner
Geometry: Plane Geometry
Law of Sines
In △ABD:
In △BCD:
By (1), (2)
Similarly
In △ABC, A = 30° and B = 45°. Find a : b : c.
First,
By the Law of Sines,
We have
Therefore,
Multiplying by 4,
In △ABC, A = 2B, a = 10, and b = 6. Find cos B.
By the Law of Sines,
Thus
Using
we get
Since B is an angle of a triangle, sin B ≠ 0, so
Therefore,
In △ABC, A = 3B and a = 2b. Find cos B.
By the Law of Sines,
Therefore,
Using
we get
Thus
Since B is a triangle angle,
We must have B = 30° rather than 150°, since A = 3B must also be an angle of the triangle.
Therefore,