Calculus - 13

Question

The area of triangle is calculated by the formula  . If the angle A is measure  with 1% error. Find the % error in area.

(A)

(B)

(C)

(D)

Answer 1

Pi / 2 . Sqrt 3

 

1/2 bc sin A  differentiating

1/2 bc cos A dA`

Comments

where pie comes ??

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dA` is error just like d theta ...So substitute it...

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please show me how u did it

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1/2 bc sin A
differentiating....
1/2 bc cos A dA*
here A = 30 degrees... A* = 1/(pie/6) .=  6/pie  (1 percent)
1/2 * sqrt 3 /  2 * 6/pie
(3*sqrt 3) / 2*pie
21 * sqrt 3 / 44 which is equal to 0.85

now come to the option pie / 2* sqrt 3
22/14*sqrt 3 approximately equal to that .....
Thats y my answer is that.

Note: Remaining options are not near to that...

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I am sorry to ask it late but how did u write "here A = 30 degrees... A* = 1/(pie/6) .=  6/pie  (1 percent)"
kindly elaborate
Also in 1/2 bc sin A
differentiating....
1/2 bc cos A dA* ( I think it should be dA, isn't it,if not why so ???))

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Hii

here 1% in 30 degrees is 1/30 degrees ... .dA=6/pie
1/2 bc are constants... differentiate sinA...... cosA dA  = cos 30  * 6/pie
then follows.....
this is not a generalised method. i just used to solve that particular problem.
If I get any other method during revison time. I will update u.

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Shouldn't be theta=pie/6 or A=pie/6,then how u wrote dA=6/pie ??

Also please answer to this "1/2 bc cos A dA* ( I think it should be dA, isn't it,if not why so ???))"

Answer 2

please chk the answer

Answer 3

please sir provide a solution..

Comments

My method:

1/2 bc sin A
differentiating....
1/2 bc cos A dA*
here A = 30 degrees... A* = 1/(pie/6) .=  6/pie  (1 percent)
1/2 * sqrt 3 /  2 * 6/pie
(3*sqrt 3) / 2*pie
21 * sqrt 3 / 44 which is equal to 0.85

now come to the option pie / 2* sqrt 3
22/14*sqrt 3 approximately equal to that .....
Thats y my answer is that.

Note: Remaining options are not near to that...

Answer 4

Therefore ans is B.