After 5 hours, how far apart are the boats? Label the distance(s) on your drawing from the first problem.

The distance between them is 277.84 m

Step-by-step explanation:

See comment for complete question.

Given

Boat A:

Boat B:

First, we calculate the distance traveled by both boats in 5 hours

For more clarity, I'll make use of the attached image to represent the system.

From the attachment, we are to calculate distance C, but first we calculate the angle between them.

C is then calculated using cosine law:

This gives:

Take square root of both sides:

The distance between them is 277.84 m

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

c

step-by-step explanation:

i think because what else can be a sample of every member