The diagonals of the figure below represent the support beams for a patio covering.

We can summarize that

By applying the law of cosines: 

c² = a² + b² - 2abcos(C) 

where: 

a,b, and c represent the triangle's sides and C denotes the angle opposing side c.

Let us assign:

a=170 miles

b=200 miles

c=160 miles

Thus, we establish: 

160² = 170² + 200² - 2(170)(200)cos(C).

We now aim to solve for C.

25,600 = 28,900 + 40,000 - 68,000cos(C).

25,600 - 28,900 - 40,000 = -68,000cos(C).

-43,300=-68,000cos(C).

Thus, cos(C)=0.6367.

C=arc cos(0.6367)--------> C=50.45°.

Consequently, the captain should adjust toward island B by

180 - 50.45 = 129.55 degrees.

The final answer is

129.55 degrees

.

I affirm that all of these statements are correct.

1,459.75 - 200.25 - 359.45 - 125.00 - 299.35 = 475.70

475.70 + 375.00 = 850.70

After settling the bills and deposit, her account shows a balance of $850.70

First note the ratio is
7:2 so divide 7 by 2 to get 7/2 = 3.5. Then add 3.5 to 2, yielding the result 5.5

The Law of Sines can be expressed as
b/sin(B) = c/sin(C)

Next, multiply both sides by sin(B).
This leads to b = (c*sin(B))/sin(C)

Thus, the correct response is C.

Answer: C. (c*sin B)/sin C