# Examples using sine rule

You can use the sine rule (If you can remember it – but why try) here it is anyway:

**Example 1**

Find the length of `x` in the following diagram?

**Solution:**

The sine rule: `a/sinA=b/sinB=c/sinC`

In a triangle that looks like:

Therefore use:

`a/sinA` | `=` | `b/sinB` |

`a/sin80` | `=` | `7/sin60` |

`a` | `=` | `(7timessin80)/sin60` |

`a` | `=` | `6.893/0.866` |

`a` | `=` | `7.959` |

Answer: `x=7.959`

**Example 2**

Find angle A

**Solution:**

The sine rule: `a/sinA=b/sinB=c/sinC`

In a triangle that looks like:

Therefore Use:

`a/sinA` | `=` | `c/sinC` |

`4.8/sinA` | `=` | `5.7/sin63` |

`(4.8timessin63)/5.7` | `=` | `sinA` |

Or

`sinA` | `=` | `(4.8timessin63)/5.7` |

`sinA` | `=` | `4.276/5.7` |

`sinA` | `=` | `0.75` |

Answer: `A=48.61^@`