Question

If in a triangle a=5 b=4 and cos(a-b) = 31/32

Answer 1

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Answer 2

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Asked on October 15, 2019 by

Novin Jaykumar

In a △ABC, if a=5,b=4 and cos(A−B)=

32

31

, then side c is

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ANSWER

Given, a=5,b=4,cos(A−B)=

32

31

Therefore, tan(

2

A−B

)=

1+cos(A+B)

1−cos(A−B)

=

63

1

⇒

a+b

a−b

cot

2

C

=

63

1

⇒

5+4

5−4

cot

2

C

=

63

1

⇒tan

2

C

=

3

7

Now, cosC=

1+tan

2

2

C

1−tan

2

2

C

⇒cosC=

1+

9

7

1−

9

7

=

8

1

Now, c

2

=a

2

+b

2

−2abcosC

⇒c

2

=25+16−40×

8

1

=36

⇒c=6