Question

7. In a right triangle ABC, ZB =90°.
(a) If AB = 6 cm, BC = 8 cm, find AC ( If AC=13 cm, BC=5 cm, find AB​

Answer 1

Given:

• Given: ABC is a right angled triangle.
• Given: ABC is a right angled triangle.Angle B = 90°

In the first condition:

AB = 6cm

BC = 8 cm

AC = ?

To find AC:

Using pythagores theorem:

H² = P² + B²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

AC = √100 = 10

Therefore, in the first case AC = 10 cm

In the second condition :

AC = 13cm

BC = 5cm

AB = ?

To find AB:

Using pythagores theorem:

H² = P² + B²

13² = AB² + 5²

169 = AB² + 25

169 - 25 = AB²

AB² = 144

AB = √144 = 12

Therefore, in the second case AB = 12cm.

Answer 2

Step-by-step explanation:

In ∆ ABC , angle B =90°

1)AB=6 cm , BC = 8 cm

By Pythagoras theorem

(AC)^2 = (AB)^2 + (BC)^2

= 6^2 + 8^2

= 36 + 64

(AC)^2 = 100

=√100

AC = 10 cm

2) AC = 13cm, BC=5cm

By Pythagoras theorem

(AC)^2 = (AB)^2 + (BC)^2

(13)^2 = (AB)^2 + (5)^2

169 = (AB)^2 + 25

(AB)^2 = 169 - 25

(AB)^2 = 144

AB = √144

AB = 12cm