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In a triangle ABC, the sides b,c are gi...

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

A

`S/(2a) Delta A`

B

`(2S)/(2a) DeltaA`

C

`bc sin A Delta A`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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]`
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