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Mathematics

Sine Rule and Cosine Rule – Trigonometry

This formula is used for solving triangles which are not right angled and in which either two angles and any side are given or two sides and the angle opposite one of them are given.

Sine Rule:

sine rule

Example 1:

Find the remaining angles of ABC in which a= 12.5cm, C= 17.7cm and C= 1160

Sine rule example 1
Sine rule example 2

Cosine Rule

The Cosine rule, just like sine rule is used to solve for the unknowns in a triangle. Cosine rule is especially use to solve triangles with the following dimension.

cosine rule
cosine rule eg3

Solution

By Cosine Rule

X2 = a2 + b2 – 2ab Cos 80

X2 = 32 + 22 -2(3)(2) x 0.1736

X2 = 13 – 2.0832

X2 = 10.9168

X2 =

=3.305cm

cosine rule eg3=4

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