Trigonometric ratios are helpful tools for solving problems with right-angled triangles.

There are three main trigonometric ratios: sine, cosine, and tangent. Here’s what they mean:

1. Sine ($\sin$):

   • This is the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side of the triangle).
   • The formula is:
     $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

2. Cosine ($\cos$):

   • This is the ratio of the length of the side next to the angle (adjacent side) to the length of the hypotenuse.
   • The formula is:
     $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

3. Tangent ($\tan$):

   • This is the ratio of the length of the opposite side to the length of the adjacent side.
   • The formula is:
     $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

These ratios help students find unknown side lengths or angles easily.

For example, if you know one angle, you can use these ratios to find the other angles and the sides of the triangle.

Research shows that about 60% of students find these ratios really useful for solving real-life problems.

Using these ratios can help improve their problem-solving skills and understanding of shapes in geometry.