Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

As the law of sines state that

                           $b *sin A = a* sin B$

So by taking derivative of both sides we get,

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

thus

                   $\frac{dB }{dA} = \frac{b*cos A }{a*cos B}$

at

        $A=$ π  / 4   & $B=$ π / 3         (using radian values for A and B)

we find

              $\frac{dB}{dA} = \sqrt{1.5}$

So,

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