IIT JEE , AIEEE Forum - Mathematics , Trignometry

tejasvi2389

If

be the area of triangle ABC and suppose a small error occurs in the measurement of c then

is given by

a)

/4[1/s + 1/s-a + 1/s-b - 1/s-c]

c

b)

/2[1/s + 1/s-a + 1/s-b - 1/s-c]

c

c)

/3[1/s + 1/s-a + 1/s-b - 1/s-c]

c

d) none

amar.gupta

when x is subject to a small increment (or a small error) of

x and y is subject to a small increment (or a small error) of

y, then the corresponding increment (or error) of

z will be given approximately by

z= (

z/

x)

x + (

z/

y)

y

now

= sqrt(s(s-a)(s-b)(s-c)) where s=a+b+c/2

so error in c causes error in s.

s= (

s/

c)

c =

c /2

now error in s and c cause error in

.

so

= (

/

s)

s + (

/

c)

c

(

/

s) = (1/2

) [

^2/s+

^2 /(s-a) +

^2 /(s-b) +

^2/(s-c)]

= (

/2) [1/s+1/(s-a) +1/(s-b) + 1/(s-c)]

and (

/

c) = (1/2

) [-

^2/(s-c)] = - (

/2) [1/(s-c)]

so

=(

/2) [1/s+1/(s-a) +1/(s-b) + 1/(s-c)] (

c /2) - (

/2) [1/(s-c)]

c

=(

c /4) [1/s+1/(s-a) +1/(s-b) + 1/(s-c) - 2/(s-c)]

=(

c /4) [1/s+1/(s-a) +1/(s-b) - 1/(s-c) ]

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