The area of a triangle is computed using the formula $S = \frac{1}{2}$ bc sin A. If the relative errors made in measuring b, c and calculating S are respectively $0.02$ , $0.01$ and $0.13$ the approximate error in A when $A = π / 6$ is

0.05

radians

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0.01

radians

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0.05

degree

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0.01

degree

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Solution

The correct option is A $0.05$ radians
Error formula for given equation is
$\frac{Δ s}{s} = \frac{Δ b}{b} + \frac{Δ c}{c} + \frac{Δ s i n x}{s i n x}$
$0.13 = 0.02 + 0.01 + \frac{Δ s i n x}{1 / 2}$
$Δ s i n x = 0.05$

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