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.

Step-by-step explanation:

(a)

Consider the following:

Use sine rule,

Again consider,

Thus, the angle B is function of A is,

Now find

Differentiate implicitly the function with respect to A to get,

b)

When , the value of is,

c)

In general, the linear approximation at x= a is,

Here the function

At

And,

from part b

Therefore, the linear approximation at is,

d)

Use part (c), when , B is approximately,

step-by-step explanation:

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb