# The sine rule

**The sine rule**

For any triangle ABC,

or

**Using the sine rule to find side lengths**

When given two angles in a triangle and the length of the opposite side of an angle, the sin rule is used to find the length go the opposite side. For example, find the length of side *a.*

*a* / sin 118° = 7 / sin 39° (rearrange)

*a* = 7 sin 118° / sin 39º

*a* = 9.82 (to 2 d.p.)

**Using the sine rule to find angles**

Similarly the sin rule can be used to find an angle of a triangle if two side lengths in a triangle are given along with the angle of the opposite side. For example, find the angle at B.

sin B / 8 = sin 46° / 6 (rearrange)

sin B = 8 sin 46° / 6

B = sin (8 sin 46° / 6)

B = sin^{-1} (8 sin 46° / 6)

B = 73.56º (to 2 d.p.)