Question

In a $\Delta ABC$ the sides b and c are given. If there is an error $\Delta A$ in measuring angle A, then the error $\Delta a$ in side a is given by

• A. $\frac{S}{2a}\Delta A$
• B. $\frac{2S}{a}\Delta A$
• C. bc sin A $\Delta A$
• D. none of these

Answer 1

The correct option is B $\frac{2S}{a}\Delta A$

In $△ABC$ we have
$\Rightarrow d\left(2bc\cos A\right)=d(b^2+c^2-a^2)\Rightarrow -2bc\sin AdA=-2ada\Rightarrow bc\sin AdA=ada$
$\Rightarrow \frac{2}{a}\left(\frac{1}{2}bc\sin B\right)dA=da$
$\Rightarrow da=\frac{2S}{a}dA$
$\Rightarrow △a=\frac{2S}{a}dA[\because dx\equiv △aanddA=BA]$