Question

In ΔABC, if a : b : c = 7 : 8: 9, then find cos A : cos B : cos C.

Answer 1

Answer:

Cos A : Cos B : Cos C = 14 : 11 : 6

Step-by-step explanation:

a : b : c = 7 : 8 : 9

Cosine Formula:

a² = b² + c² - 2bcCos (A)

Find cos(A):

a² = b² + c² - 2bcCos (A)

Cos A = (b² + c² - a²)/2bc

Cos A = (8² + 9² - 7²)/2(8)(9)

Cos A = 96/144 = 2/3

FInd Cos (B):

b² = a² + c² - 2acCos (B)

Cos B = (a² + c² - b²)/2ac

Cos B = (7² + 9² - 8²)/2(7)(9)

Cos B = 66/126 = 11/21

FInd Cos (C):

c² = a² + b² - 2abCos (C)

Cos C = (a² + b² - c²)/2ab

Cos C = (7² + 8² - 9²)/2(7)(8)

Cos C = 32/112 = 2/7

Find the ratio:

Cos A = 2/3 = 14/21

Cos B = 11/21

Cos C = 2/7 = 6/21

Cos A : Cos B : Cos C = 14/21 : 11/21 : 6/21

Multiply by 21:

Cos A : Cos B : Cos C = 14 : 11 : 6

Answer: Cos A : Cos B : Cos C = 14 : 11 : 6