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.
What is the value of the angle ABC?
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
Answer: 45º
What is the value of the angle BAC?
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
Answer: 60º