In the triangle \( ABC \), \( |AB| = 2 \) and \( |BC| = 1 \) - Junior Cycle Mathematics - Question a - 2013

Using the Pythagorean theorem, we have:

$h^2 = a^2 + b^2$

Here, the sides are given as follows:

• ( |AB| = 2 )
• ( |BC| = 1 )

Thus, we can express ( |AC| ) as follows:

$2^2 = |AC|^2 + 1^2$

This simplifies to:

$4 = |AC|^2 + 1$

Subtracting 1 from both sides gives:

$|AC|^2 = 3$

Taking the square root:

$|AC| = \sqrt{3}$