If in a ∆ABC , a = 6 cm , b = 8 cm , c = 10 cm, then the value of sin 2A is

1) 6/25

2) 8/25

3) 10/25

4) 24/25

Solution:

Given a = 6 cm , b = 8 cm , c = 10 cm

From cosine rule cos A = (b² + c² – a²)/2bc

= (8² + 10² – 6²)/2×8×10

= (64 + 100 – 36)/160

= 128/160

= 4/5

sin A = √(1 – cos² A)

= √(1 – 16/25)

= 3/5

sin 2A = 2 sin A cos A

= 2×3/5 × ⅘

= 24/25

Hence option (4) is the answer.