Question

In a right triangle ABC, \(∠ B\) = 90°. 

1. If AB = 6 cm, BC = 8 cm, find AC 
2.  If AC = 13 cm, BC = 5 cm, find AB

Answer 1

(a) \(\triangle ABC\) is right-angled at \(B\).
Therefore, by applying Pythagoras theorem, we obtain
\(AC^2 = AB^2 + BC^2\)
\(AC^2 = (6 cm)^2 + (8 cm)^2\)
\(AC^2 = (36 + 64) cm^2\)
=\(100\) \(cm^2\)
\(AC = (\sqrt{100}) cm = (\sqrt{10 × 10}) cm\)
\(AC = 10 \;cm\)

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(b) \(\triangle ABC\) is right-angled at \(B\).
Therefore, by applying Pythagoras theorem, we obtain
\(AC^2 = AB^2+ BC^2\)
\((13 cm)^2= (AB)^2+ (5 cm)^2\)
\(AB^2= (13 cm)^2- (5 cm)^2\)
=\( (169 - 25) cm^2\)
= \(144 \;cm^2\)
\(AB = (\sqrt{144}) cm = (\sqrt{12 × 12}) \,cm\)
\(AB = 12 \;cm\)