Question

In a right triangle ABC, ∴ B = 90°.

(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

Answer 1

(a) ΔABC is right-angled at B.

Therefore, by applying Pythagoras theorem, we obtain

AC² = AB² + BC²

AC² = (6 cm)² + (8 cm)2

AC² = (36 + 64) cm² =100 cm2

AC = (√100) cm = (√10x10) cm

AC = 10 cm

(b) ΔABC is right-angled at B.

Therefore, by applying Pythagoras theorem, we obtain

AC² = AB² + BC²

(13 cm)² = (AB)² + (5 cm)²

AB² = (13 cm)² − (5 cm)² = (169 − 25) cm² = 144 cm2

AB = (√144) cm = (√12x12) cm

AB = 12 cm