Given (b+c/11) = (c+a/12)= (a+b/13) for a Δ ABC with usual notation. If ( cos A/α) = ( cos B/β) = ( cos C/γ) , then the ordered triad ( α, β, γ) has a value :

Question

Given (b+c/11) = (c+a/12)= (a+b/13) for a Δ ABC with usual notation. If ( cos A/α) = ( cos B/β) = ( cos C/&gamma;) , then the ordered triad ( α, β, &gamma;) has a value : (A) (3, 4, 5) (B) (19, 7, 25) (C) (7, 19, 25) (D) (5, 12, 13)

Tardigrade Admin · Accepted Answer

b + c = 11 λ , c + a = 12 λ, a + b = 13 λ ⇒ a = 7 λ , b = 6 λ , c = 5λ (using cosine formula) cos A =(1/5) , cos B = (19/35) , cos C = (5/7) α: β:&gamma; ⇒ 7: 19: 25

Q. Given $\frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13}$ for a $Δ A BC$ with usual notation. If $\frac{c o s A}{α} = \frac{c o s B}{β} = \frac{c o s C}{γ}$ , then the ordered triad $(α, β, γ)$ has a value :

(3, 4, 5)

(19, 7, 25)

(7, 19, 25)

(5, 12, 13)

$b + c = 11 λ, c + a = 12 λ, a + b = 13 λ$
$\Rightarrow a = 7 λ, b = 6 λ, c = 5 λ$
(using cosine formula)
$cos A = \frac{1}{5}, cos B = \frac{19}{35}, cos C = \frac{5}{7}$
$α : β : γ \Rightarrow 7 : 19 : 25$

Q. Given 11b+c​=12c+a​=13a+b​ for a ΔABC with usual notation. If αcosA​=βcosB​=γcosC​ , then the ordered triad (α,β,γ) has a value :