Question

In a $\Delta ABC$ if sides a and b remain constant such that $\alpha$ is the error in C, then relative error in its area is

• A. $\alpha \cot C$
• B. $\alpha \sin C$
• C. $\alpha \tan C$
• D. $\alpha \cos C$

Answer 1

The correct option is A $\alpha \cot C$

Area of triangle $S=\frac{1}{2}ab\sin C$

$\Rightarrow \frac{dS}{dC}=\frac{1}{2}ab\cos C$

Now, approximate error in S is $\Delta S=\frac{dS}{dC}\Delta C$

$\Rightarrow \Delta S=\frac{1}{2}ab\cos C\alpha [\because \Delta C=\alpha ]$

$\Rightarrow \frac{\Delta S}{S}=\frac{\frac{1}{2}ab\cos C}{\frac{1}{2}ab\sin C}\alpha =\alpha \cot C$