The area of a triangle is `A = frac(1)(2)bh`, where `b` is the base length and `h` is the *vertical height*.

Using the trigonometrical ratios, the vertical height `h = a xx sin C`.

Substituting into the formula for the area of a triangle when the vertical height is known:

`A = frac(1)(2) xx b xx h`

`A = frac(1)(2) xx b xx a xx sin C`

`A = frac(1)(2)ab sin C`

What is the area of the triangle, below? Give your answer correct to 2 decimal places.

Area of a triangle | `A` | `= frac(1)(2)ab sin C` |

substitute | `= frac(1)(2)(14)(19) sin (68)` | |

`= 123.3155` | ||

to 2 dp | `= 123.32` |

Answer: 123.32 cm^{2}

The area of the triangle below is 100 cm^{2}. What is the size of the angle *x*? Give your
answer correct to the nearest degree.

Area of a triangle | `A` | `= frac(1)(2)ab sin C` |

substitute | `100` | `= frac(1)(2)(18)(20) sin x` |

`100` | `= 180 sin x` | |

`0.55556` | `= sin x` | |

sin^{-1} both sides |
`sin^-1(0.55556)` | `= x` |

`33.749` | `= x` | |

nearest degree | `34` | `= x` |

Answer: 34ยบ

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