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According to the ``law of sines,'' you always have: b a = sinB sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is π/4 radians=45o and the angle B is π/3 radians = 60o. You then widen A to 46o, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B.

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umairfeb221999

Answer:

The angle of B ≈ π / 3 + √1.5 ( π / 180) radians.

Step-by-step explanation:

As the law of sines state that

                           [tex]b *sin A = a* sin B[/tex]

So by taking derivative of both sides we get,

                    [tex]b*cos A = a*cos B* [ \frac{dB }{dA} ][/tex]

thus

                   [tex]\frac{dB }{dA} = \frac{b*cos A }{a*cos B}[/tex]

at

        [tex]A=[/tex] π  / 4   & [tex]B=[/tex] π / 3         (using radian values for A and B)

we find

              [tex]\frac{dB}{dA} = \sqrt{1.5}[/tex]

So,

                  B ≈ π / 3 + √1.5 ( π / 180)

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