In a right triangle ABC, ∠ B = 90°, (i) If AB = 6 cm, BC = 8 cm, find AC
(ii) If AC = 13 cm, BC = 5 cm, find AB

Solution:

In a right-angled triangle if two sides are given then the third side can be calculated using the Pythagoras theorem.

Given that, in the right triangle ABC, ∠ B = 90°, thus AC is the hypotenuse

(i)  AB = 6 cm, BC = 8 cm, AC = ?

According to Pythagoras theorem, 

AC² = AB² + BC²

AC² = (6)² + (8)²

AC² = 100

AC = √100 = 10 cm

(ii) AC = 13 cm, BC = 5 cm, AB = ?

According to Pythagoras theorem

AC² = AB² + BC²

(13)² = AB² + (5)²

169 = AB² + 25

AB² = 169 - 25 = 144

AB = √144 = 12 cm

Therefore, the length of sides AC and sides AB in the respective right triangles are AC = 10 cm and AB = 12 cm.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.4 Question 7

Summary:

In a right triangle ABC, ∠B = 90°. (a) If AB = 6 cm, BC = 8 cm, AC will be 10 cm (b) If AC = 13 cm, BC = 5 cm, AB will be 12 cm.

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