Confusing opposite and adjacent sides

❌ The Mistake in Action

In a right-angled triangle, angle θ = 40°. The side next to θ (not the hypotenuse) is 8cm. Find the side opposite θ.

Wrong: "Adjacent = unknown, Opposite = 8" $\tan(40°) = \frac{8}{x}$

🧠 Why It Happens

Students confuse which side is "opposite" and which is "adjacent." They may label based on how the triangle looks rather than relative to the specific angle.

✅ The Fix

Always label from YOUR angle:

Opposite: Directly across from θ (doesn't touch θ)
Adjacent: Next to θ (touches θ, but isn't the hypotenuse)
Hypotenuse: Opposite the right angle (longest side)

In this problem, from θ = 40°:

The side "next to θ" = Adjacent = 8cm
The side "opposite θ" = Opposite = x

$$\tan(40°) = \frac{x}{8}$$ $$x = 8 \times \tan(40°) = 6.71\text{cm}$$

🔍 Spot the Mistake

Can you identify where this student went wrong?

Angle = 40°. Side next to θ is 8cm. Find the opposite side.

Opposite = 8cm, Adjacent = x

$\tan(40°) = \frac{8}{x}$

Click on the line that contains the error.

📚 Related Topics

Learn more about the underlying maths: