The area of a triangle is computed using the formula s=12bc 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

The area of a triangle is computed using the formula s=12bc 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

  1. A

    0.05 radians 

  2. B

    0.01 radians

  3. C

    0.05 degree

  4. D

    0.01 degree

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    Solution:

    We have,

    S=12bcsinAdS=12d(bcsinA)dS=12{csinAdb+bsinAbc+bccosAdA}dSS=dbb+dcc+cotAdA0.13=0.02+0.01+cotπ6dA               dSS=0.13,dbb=0.020.10=3dAdA=0.103=0.05 radians 

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