Kabulongagirls/Trigonometry/Chapter 2/THE SINE RILE

From WikiEducator
Jump to: navigation, search

The Sine Rule

Let us now look at the Sine Rule

Icon objectives.jpg
At the end of this session we should be able to
  • state the sine rule
  • apply Sine Rule to calculate the lengths of sides of an angle
  • apply Sine Rule to calculate the sizes of angles
  • apply Sine Rule to solve word problems

The law of sines (sines law, sine formula, sine rule), in trigonometry, is a statement about any triangle in a plane. Where the sides of the triangle are a, b and c and the angles opposite those sides are A, B and C, then the law of sines states:

[math]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = [/math]

where R is the radius of the triangle's circumcircle. This law is useful when computing the remaining sides of a triangle if two angles and a side are known, a common problem in the technique of triangulation. It can also be used when two sides and one of the non-enclosed angles are known; in this case, the formula may give two possible values for the enclosed angle. When this happens, often only one result will cause all angles to be less than 180°; in other cases, there are two valid solutions to the triangle