Question

If a=4,b=5,c=7 then find cos B/2

Answer 1

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Answer 2

Given :

For Any Triangle with angles

The value of a = 4

The value of b = 5

The value of c = 7

To Find :

The measure of Cos$\dfrac{B}{2}$

Solution :

For Any Triangle with angles

∵ Cos$\dfrac{B}{2}$  = $\sqrt{\dfrac{S(S-c)}{a b}}$                  ..........1

where   S = $\dfrac{a+b+c}{2}$

               = $\dfrac{4+5+7}{2}$

               = $\dfrac{16}{2}$  = 8

Now, Putting the value of S into eq 1

Cos$\dfrac{B}{2}$  = $\sqrt{\dfrac{S(S-c)}{a b}}$      

           = $\sqrt{\dfrac{S\times (S-c)}{a\times b}}$

           = $\sqrt{\dfrac{8\times (8-7)}{4\times 5}}$

            = $\sqrt{\dfrac{8\times 1}{4\times 5}}$

            = $\sqrt{\dfrac{2}{ 5}}$

Hence, The value of  Cos$\dfrac{B}{2}$ is $\sqrt{\dfrac{2}{ 5}}$   Answer