Trigonometry links angles to side lengths in triangles. For right-angled triangles, you use SOHCAHTOA — the three ratios linking an angle to the sides of the triangle are shown in the poster above.
The first step is always to label the sides relative to your angle θ:
Hypotenuse: the longest side (opposite the right angle)
Opposite: the side directly opposite your angle
Adjacent: the side next to your angle (that isn't the hypotenuse)
To find a missing side: choose the right trig ratio, substitute, rearrange.
To find a missing angle: use the inverse function (sin−1, cos−1, or tan−1).
The exact trig values for 30°, 45° and 60° (shown in the reference table above) MUST be memorised — they come up very often on non-calculator papers!