About Law of Sines
The law of sines provides the link between an oblique triangle's sides and angles (non-right triangle). In trigonometry, the laws of sines and cosines are key rules for "solving a triangle." The sine rule states that the ratios of a triangle's side lengths to the sine of its respective opposite angles are equal.
What do you mean by Law of Sines?
The law of sines connects the ratios of triangle side lengths to their opposing angles. For all three sides and opposite angles, this ratio remains constant. Using the needed known data, we can use the sine rule to find the missing angle or side of any triangle.
Law of Sines
The diameter of the circumcircle of a triangle is equal to the ratio of the side and the corresponding angle. As a result, the sine law can be written as,
a/sinA = b/sinB = c/sinC = 2R
- The lengths of the triangle's sides are a, b, and c.
- The triangle's angles are A, B, and C.
- The radius of the triangle's circumcircle is R.
Law of Sines Formula
For linking the lengths of a triangle's sides to the sines of consecutive angles, the law of sines formula is utilised. It is the ratio of the length of one of the triangle's sides to the sine of the angle generated by the remaining two sides. Apart from SAS and SSS triangles, the law of sines formula is applied to any triangle. It says,
a/sin A = b/sin B = c/sin C
where a, b, and c are the triangle's lengths and A, B, and C are the triangle's angles. This formula can be written in three different ways, as follows:
a/sinA = b/sinB = c/sinC
sinA/a = sinB/b = sinC/c
a/b = sinA/sinB; a/c = sinA/sinC; b/c = sinB/sinC
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