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,

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

explanation:

step-by-step explanation: