Question

The perimeter of a triangle ABC is 6 times the arithmetic mean
of the sines of its angles. If the side bis 2, then the angle B is
​

Answer 1

We have a+b+c=

3

6(sinA+sinB+sinC)

⇒k(sinA+sinB+sinC)=2(sinA+sinB+sinC),

where K=

sinA

a

=

sinB

b

=

sinC

c

⇒K=2 ......(∵sinA+sinB+sinC



=0)

⇒

sinA

a

=2

⇒sinA=

2

1

⇒A=

6

π

Step-by-step explanation:

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