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TS EAMCET · Maths · Application of Derivatives

In a \(\triangle A B C\), the sides \(b, c\) are fixed. In measuring angle \(A\), if there is an error of \(\delta \mathrm{A}\), then the percentage error in measuring the length of the side \(a\) is

  1. A \(\frac{2 \Delta \delta A}{R \sin A} \times 100\)
  2. B \(2 \times \frac{\delta A}{A} \times 100\)
  3. C \(\frac{\Delta \delta A}{2 R^2 \sin ^2 A} \times 100\)
  4. D \(\frac{\Delta^2 \delta A}{R \sin A} \times 100\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\Delta \delta A}{2 R^2 \sin ^2 A} \times 100\)

Step-by-step Solution

Detailed explanation

\(\begin{gathered}\cos \mathrm{A}=\frac{b^2+c^2-a^2}{2 b c} \\ \Rightarrow 2 \mathrm{bc} \cos \mathrm{A}=b^2+c^2-a^2\end{gathered}\) Differentiate both sides w.r.t a \(2 b c \sin A S A=-20 \delta a\) \(\Rightarrow \delta_E=\frac{b c \sin \mathrm{~A} \mathbb{A}}{a}\)..(i) Area…