#17
Top 50 Mistake
Labelling the wrong side as the hypotenuse
"The Hypotenuse Hijack"
The Mistake in Action
Find side $x$ in a right-angled triangle where the sides adjacent to the right angle are 6cm and $x$, and the side opposite the right angle is 8cm.
Wrong: $8^2 + 6^2 = x^2$ $x = 10$ cm
Why It Happens
Students don't correctly identify which side is the hypotenuse. They may default to making the unknown side the hypotenuse.
The Fix
The hypotenuse is:
- Always opposite the right angle
- Always the longest side
- Never touches the right angle
In this question, 8cm is opposite the right angle, so 8cm is the hypotenuse.
$$6^2 + x^2 = 8^2$$ $$36 + x^2 = 64$$ $$x^2 = 28$$ $$x = \sqrt{28} = 5.29\text{cm}$$
Spot the Mistake
Can you identify where this student went wrong?
The side opposite the right angle is 8cm. The other sides are 6cm and x. Find x.
$8^2 + 6^2 = x^2$
$x = 10$ cm
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: