Using the wrong trigonometric rule H
"The Rule Mix-Up"
The Mistake in Action
In triangle ABC, angle A = 50°, side b = 8cm, and side c = 10cm. Find side a.
Wrong: Using the sine rule: $\frac{a}{\sin 50°} = \frac{8}{\sin B}$
But we don't know angle B, so we're stuck.
Why It Happens
Students remember the sine rule is "easier" and try to use it without checking if they have the right information.
The Fix
Use the decision tree:
- Do you have a matching pair (angle + opposite side)? → Sine Rule
- Do you have two sides and the included angle? → Cosine Rule
In this problem: We have angle A (50°) and the two sides that include angle A (b and c). That's the cosine rule setup!
$$a^2 = b^2 + c^2 - 2bc\cos A$$ $$a^2 = 8^2 + 10^2 - 2(8)(10)\cos 50°$$ $$a^2 = 64 + 100 - 160(0.6428)$$ $$a^2 = 61.15...$$ $$a = 7.82\text{cm}$$
Spot the Mistake
Can you identify where this student went wrong?
In triangle ABC, angle A = 50°, side b = 8cm, side c = 10cm. Find side a.
Using the sine rule: $\frac{a}{\sin 50°} = \frac{8}{\sin B}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: