The angle C of ∆ABC is found by measurement to be and the area is calculated by the formula 12 ab sin C. The percentage error in the calculated area due to an error 101 in the measured value of C is

∠C=470 601=10 11=π180×160 101=π180×6=δc A=12 ab sin c log A=log 12 ab+log sin c 1A δA=1sin c cos c δC δAA×100=cot c δc×100 =cot 47×π180×6×100=5π54 cot 470

The angle C of ∆ABC is found by measurement to be and the area is calculated by the formula 12 ab sin C. The percentage error in the calculated area due to an error 101 in the measured value of C is

∠C=470 601=10 11=π180×160 101=π180×6=δc A=12 ab sin c log A=log 12 ab+log sin c 1A δA=1sin c cos c δC δAA×100=cot c δc×100 =cot 47×π180×6×100=5π54 cot 470

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The angle $C$ of $∆ ABC$ is found by measurement to be and the area is calculated by the formula $\frac{1}{2} ab$ sin $C$ . The percentage error in the calculated area due to an error $10^{1}$ in the measured value of $C$ is

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$\frac{5 π}{54} \cot 47^{\circ}$

$\frac{πbc}{1440} \cot 63^{\circ}$

$\frac{5 π}{36} \cot 63^{\circ}$

$\frac{πbc}{1120} \cos 42^{\circ}$

answer is A.

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Detailed Solution

$∠ C = 47^{0} 60^{1} = 1^{0} 1^{1} = \frac{π}{180 \times 160} 10^{1} = \frac{π}{180 \times 6} = δ c A = \frac{1}{2} ab \sin c \log A = \log \frac{1}{2} ab + \log \sin c \frac{1}{A} δ A = \frac{1}{\sin c} \cos c δ C \frac{δ A}{A} \times 100 = \cot c δ c \times 100 = \cot 47 \times \frac{π}{180 \times 6} \times 100 = \frac{5 π}{54} \cot 47^{0}$