Identify the triangle and known sides.

a) Find the size of angle ABC.

Step 1: Identify the triangle and known sides.
We are given $\triangle ABC$ with sides $AB = 5 \, cm$, $BC = 8 \, cm$, and diagonal $AC = 10 \, cm$.

Step 2: Apply the Cosine Rule to find $\angle ABC$.
The Cosine Rule states $c^2 = a^2 + b^2 - 2ab \cos C$. In $\triangle ABC$, we want to find $\angle ABC$, so we use $AC^2 = AB^2 + BC^2 - 2(AB)(BC) \cos(\angle ABC)$.

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