Calculus-In-AB-C-B-2-C-a-b-then-specify-the-limits-of-the-changes-

Question Number 144662 by mnjuly1970 last updated on 27/Jun/21

\dots \dots \dots . . Calculus \dots \dots \dots . .

In A \overset{Δ}{B C} :

\hat{B} = 2 \hat{C}, a = λ b t h e n s p e c i f y

t h e l i m i t s o f t h e c h a n g e s^{'} λ^{'} :

Answered by mindispower last updated on 27/Jun/21

\frac{a}{b} = λ

\frac{a}{s i n (A)} = \frac{b}{s i n (B)} = \frac{c}{s i n (C)}

λ = \frac{s i n (π - (3 c))}{s i n (2 c)} = \frac{s i n (3 c)}{s i n (c)}

s i n (3 c) = 3 s i n (c) - 4 {s i n}^{2} (c)

λ = 3 - 4 {s i n}^{2} (c)

A + B + C = π

A + 3 C = π

A = π - 3 C > 0 \Rightarrow 0 < C < \frac{π}{3}

{s i n}^{2} (C) ⩽ {s i n}^{2} (\frac{π}{3}) = \frac{3}{4}

λ ⩾ 3 - \frac{4.3}{4} = 0

λ \in] 0, 3 [