The diagram shows triangle $ABC$ with $AB=9$ cm, $AC=12$ cm and $BC=15$ cm. The perpendicula

Question

The diagram shows triangle $ABC$ with $AB=9$ cm, $AC=12$ cm and $BC=15$ cm. The perpendicular distance from $A$ to $BC$ is $d$. Prove that $ABC$ is right-angled. Find $d$.

Accepted Answer

(a) $9^2+12^2=15^2$, so $\angle A=90^\circ$; (b) $d=7.2$ cm.

Right-triangle proof and altitude

Right-triangle proof and altitude

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