In the triangle pictured, let a, b, c be the angles at the three vertices, and let a, b,c be the sides opposite those angles. 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. notice that the angle b is a function of the angle a; i. e. b=f(a). consequently, it makes sense to calculate the implicit derivative: a. db/da? b. write the linear approximation of f