The SOH-CAH-TOA tool is a simple way for Year 12 students to remember the basic trigonometric ratios: Sine, Cosine, and Tangent.

These ratios help us understand right triangles.

Here’s what each part means:

• SOH: Sine = Opposite side / Hypotenuse
• CAH: Cosine = Adjacent side / Hypotenuse
• TOA: Tangent = Opposite side / Adjacent side

But how do we use these ratios in everyday life?

1. Engineering: Engineers use SOH-CAH-TOA to figure out forces on buildings and bridges. For example, if they know the angle of a beam and its length, they can find out how high it reaches using sine.

2. Navigation: Pilots and sailors calculate distances and angles when planning their trips. By figuring out the angle between two points, they can safely find their way using trigonometric ratios.

3. Architecture: Architects use these ratios to design strong and good-looking buildings. They can accurately calculate slopes and heights to make sure everything is stable.

For example, if a ladder is leaning against a wall at a $30^\circ$ angle, we can use the sine ratio and the ladder’s length to find out how high it goes up the wall.

SOH-CAH-TOA shows us how trigonometric ratios can help solve real-world problems easily!