GCSE(F), GCSE(H),

The trigonometric values of certain angles should be known:

Angle | Sin | Cos | Tan |
---|---|---|---|

0º | 0 | 1 | 0 |

30º | `frac(1)(2)` | `frac(√3)(2)` | `frac(1)(√3)` |

45º | `frac(1)(√2)` | `frac(1)(√2)` | 1 |

60º | `frac(√3)(2)` | `frac(1)(2)` | `sqrt(3)` |

90º | 1 | 0 | undefined |

The entry for tan 90º is undefined as the value is infinity.

1. What is the value of the angle ABC?

Answer: 45º

The adjacent and opposite values are known. The tan of an angle is given by `frac(text(opp))(text(adj))` = `frac(2)(2)` = 1. The angle with a tan value of 1 is 45º

2. What is the value of the angle BAC?

Answer: 60º

The hypotenuse and opposite sides are known.

The sine of the angle is given by `frac(text(opp))(text(hype))` = `frac(sqrt(3))(2)` = 60º

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