# 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,

AC^{2} = AB^{2} + BC^{2}

AC^{2} = (6)^{2} + (8)^{2}

AC^{2} = 100

AC = √100 = 10 cm

(ii) AC = 13 cm, BC = 5 cm, AB = ?

According to Pythagoras theorem

AC^{2} = AB^{2} + BC^{2}

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

169 = AB^{2} + 25

AB^{2} = 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.

**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.