Using the wrong angle in the area formula H
"The Wrong Angle"
The Mistake in Action
Triangle PQR has PQ = 8cm, QR = 12cm, and angle P = 35°. Find the area.
Wrong: Area $= \frac{1}{2} \times 8 \times 12 \times \sin 35°$ Area $= 48 \times 0.574$ Area $= 27.5\text{cm}^2$
Why It Happens
Students use the area formula with any angle, not realising the angle must be between the two sides being used.
The Fix
The area formula is $\frac{1}{2}ab\sin C$, where angle $C$ is between sides $a$ and $b$.
In this problem:
- Sides used: PQ (8cm) and QR (12cm)
- These sides meet at point Q
- We need angle Q, not angle P!
You would need to:
- Use the sine rule to find another angle, OR
- Use cosine rule to find side PR, then use sine rule, OR
- Be given angle Q directly
Spot the Mistake
Can you identify where this student went wrong?
Triangle PQR has PQ = 8cm, QR = 12cm, angle P = 35°
Area $= \frac{1}{2} \times 8 \times 12 \times \sin 35°$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: