Question
In a $\triangle \text{ABC},$ AD is the altitude from A such that AD = 12cm. BD = 9cm and DC = 16cm. Examine if $\triangle \text{ABC},$ is right angled at A.
✓
Answer
In $\triangle ADC$,
$\angle ADC =90^{\circ}$ ( AD is an altitude on BC )
Using the Pythagoras theorem, we get:
$12^2+16^2=AC^2$
$AC C^2=144+256$
$=400$
$AC=20 cm$
In $\triangle ADB,$
$\angle ADB=90^{\circ}$
( AD is an altitude on BC )
Using the Pythagoras theorem, we get:
$12^2+9^2=A B^2$
$A B^2=144+81$
$=225$
$A B=15 cm$
In $\triangle ABC, $
$BC^2=25^2=625$
$AB^2+AC^2$
$=15^2+20^2$
$=625$
$AB^2+AC^2=BC^2$
Because it satisfies the Pythagoras theorem, we can say that $\triangle ABC$, is right angled at A .
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