The area of a triangleis computed using the formula `S=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=pi//6`, is

Options

A. 0.05 radians
B. 0.01 radians
C. 0.05 degree
D. 0.01 degree

Answer

A

Explanation

We have, `S=1/2bc sin A`
`rArr" "dS=1/2" "d(bc sin A)`
`rArr" "dS=1/2 {c sin A db + b sin A" "bc + bc cos A" dA}`
`rArr" "(dS)/S=(db)/b+(dc)/c+cot A" "dA`
`rArr" "0.13=0.02 + 0.01+ cot.(pi)/6 dA" "[:' (dS)/S=0.13, (db)/b=0.02and (dC)/c=0.01]`
`rArr" "0.10=sqrt(3) dA`
`rArr" "dA=(0.10)/sqrt(3)=0.05 radians`