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Question

If in a ABC, 4sinA=4sinB=3sinC, then cosC is equal to


A

13

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B

19

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C

127

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D

18

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Solution

The correct option is B

19


Explanation for the correct option.

Find the value of cosC:

Given,

4sinA=4sinA=3sinC.

Let 4sinA=4sinB=3sinC=k

sinA=k4,sinB=k4and sinC=k3.

Now use sine rule,

asinA=bsinB=csinC=λa=λsinA,b=λsinB,c=λsinC

Substituting the values of sinA,sinBand sinC.

a=λk4,b=λk4,c=λk3

Let, λk=p.

a=p4,b=p4,c=p3

Now, we know that,

cosC=a2+b2-c22ab

Substituting the values of a,b and c.

cosC=p42+p42-p322p4p4=p216+p216-p29p28=116+116-1918=19

Hence, the correct option is B.


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