Question

in triangle ABC if b=24,c=20 and sin A/2=1/√8,find a

Answer 1

Answer:

a = 16

Step-by-step explanation:

in triangle ABC if b=24,c=20

Sin(A/2) = 1/√8

in triangle ABC

a² = b² + c² - 2bc CosA

=> a² = 24² + 20² - 2*24*20CosA

=> a² = 576 + 400 - 960CosA

=> a² = 976 - 960CosA

CosA = 1 - 2Sin²(A/2)

=> CosA = 1 - 2(1/8)

=> CosA = 1 - 1/4

=> CosA = 3/4

using this value

a² = 976 - 960(3/4)

=> a² = 976 - 720

=> a² = 256

=> a = 16