In a triangle `ABC`, the sides `b,c` are given. If there is an error `deltaA` in measuring angle A.Then side a is error `deltaa` in the side a is

Options

A. `S/(2a) Delta A`
B. `(2S)/(2a) DeltaA`
C. `bc sin A Delta A`
D. none of these

Answer

B

Explanation

In `Delta` ABC, we have
`2bc" "cos A=b^(2) +c^(2)-a^(2)` ,
`rArr" "d(2bc" "cos A)= d(b^(2)+c^(2)-a^(2))`
`rArr" "-2bc" "sin" " A" "dA=-2a" "da`
`rArr" "bc" "sin A" "=a" "da`
`rArr" "2/a(1/2bc" "sinA)dA=da`
`rArr" "da=(2S)/a dA`
`rArr" "Deltaa=(2S)/a DeltaA`" "[:' da cong Deltaa and dA cong DeltaA]`