Question

In ∆ABC, if a = 2b and A = 3B, then the value of c/b is equal to
(A)3
(B)√2
(C) 1
(D)√3
​

Answer 1

Answer: (d)

Step-by-step explanation:

2sinB=sin3B

2sinB=3sinB−4sin  

3

1  

3

 

sinB[4sin  

2

B−1]=0

sinB=0 or  sin  

2

B=  

4

1

​  

 

sin  

2

B=(  

2

1

​  

)  

2

 

sinB=  

2

1

​  

 

B=  

6

π

​  

×  

π

180

​  

=30  

∘

 

B=30

A=3×30  

∘

 

A=90  

∘

 

C=180−(90+30)

=180−120

=60

∴  

b

c

​  

=  

sinB

sinC

​  

=  

sin30  

∘

 

sin60  

∘

 

​  

=  

3

​