Trigonometric ratios are really useful for finding missing sides in right-angled triangles. Here’s how you can use them:

1. Identify the Triangle: Start by labeling the sides based on the angle you know. You’ll have three sides:

   • Opposite: the side across from the angle
   • Adjacent: the side next to the angle
   • Hypotenuse: the longest side, which is always across from the right angle

2. Choose the Right Ratio: Depending on which sides you have, pick one of these ratios:

   • Sine (sin): This ratio compares the opposite side to the hypotenuse.

     • Formula: ( sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} )

   • Cosine (cos): This one compares the adjacent side to the hypotenuse.

     • Formula: ( cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} )

   • Tangent (tan): This ratio looks at the opposite side compared to the adjacent side.

     • Formula: ( tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} )

3. Rearrange to Solve: If you know one side of the triangle and the angle, you can rearrange these ratios to find the missing side.

Using trigonometry can make these problems a lot easier. Plus, it's really satisfying to see everything come together!