The-perimeter-of-a-ABC-is-6-times-the-arithmetic-mean-of-the-sines-of-its-angles-If-the-side-a-is-1-then-the-angle-A-is-

Question Number 94628 by Vishal Sharma last updated on 20/May/20

The perimeter of a △ A B C is 6 times

the arithmetic mean of the sines of

its angles . If the side a is 1, then the

angle A is

Answered by Kunal12588 last updated on 20/May/20

(a + b + c) = 6 \times \frac{1}{3} (s i n A + s i n B + s i n C)

\frac{s i n A}{a} = \frac{s i n B}{b} = \frac{s i n C}{c} = k [s i n e r u l e]

(a + b + c) = 2 k (a + b + c)

\Rightarrow k = \frac{1}{2}

\Rightarrow s i n A = \frac{a}{2}

\Rightarrow A = {s i n}^{- 1} \frac{1}{2} [∵ a = 1]

\Rightarrow A = \frac{π}{6} = 30 °