To chart the movement of a polar bear, scientists attached a radio transmitter to its neck. Two tracking stations are monitoring the radio signals from the bear. Station B is 10 miles directly east of station A. On Monday, station A measured the direction to the bear at N43E,and station B at N30W. Three days later the directions to the bear from the two tracking stations were N24E and N30W,respectively. How much farther from station B was the polar bear after those three days?

Question

To chart the movement of a polar bear, scientists attached a radio transmitter to its neck. Two tracking stations are monitoring the radio signals from the bear. Station B is 10 miles directly east of station A. On Monday, station A measured the direction to the bear at N43E,and station B at N30W. Three days later the directions to the bear from the two tracking stations were N24E and N30W,respectively. How much farther from station B was the polar bear after those three days?

Answer 1

Initial position of bear at C

final position of bear at D
angle CAB = 90-43 = 47
angle CBA = 90-30 = 60
therefore angle ACB = 180-47-80 = 73
sin 60/AC = sin 73/10
AC = 10 sin 60 /sin 73
do that
then
angle DAC = 43-24 = 19
angle DCA = 180 - 73 = 180-73 = 107
angle ADC = 180 -19 -107 = 54
so
sin 19/DC = sin 54 / AC
and we know AC

Answer 2

To solve this problem, we need to calculate the distance traveled by the polar bear between the two sets of measurements. We can use the direction and distance information to determine the displacement of the bear relative to each tracking station.

Let's break down the given information:

1. On Monday, station A measured the bear's direction as N43E, and station B measured the direction as N30W.
- This means that the bear was, on Monday, a certain distance away (let's call it "x") from station A in the direction N43°E, and a certain distance away (also "x") from station B in the direction N30°W.

2. Three days later, station A measured the direction as N24°E, and station B measured the direction as N30°W.
- This means that the bear had moved a certain distance (let's call it "y") from station A in the direction N24°E, and it had moved a certain distance (also "y") from station B in the direction N30°W.

Now, we need to find the values of "x" and "y" to calculate the displacement of the bear from each station:

For station A:
- The bear started at x distance away from station A and moved y distance away from it.
- To find the displacement from station A after three days, we subtract the initial distance (x) from the final distance (y): y - x.

For station B:
- The bear started at x distance away from station B and moved y distance away from it.
- To find the displacement from station B after three days, we subtract the initial distance (x) from the final distance (y): y - x.

Now, we can calculate the displacement from each station:

Displacement from station A: (N24°E - N43°E)
- To subtract two angles, we subtract the first angle from 360° and add the second angle.
- 360° - 43° + 24° = 341°.
- Keep in mind that this displacement is independent of distance and only gives us the direction change.

Displacement from station B: (N30°W - N30°W)
- The bear didn't change its direction relative to station B. We don't need to calculate displacement here as it is zero.

Considering the displacement values, we can conclude that the bear moved closer to station A and remained at the same distance from station B.

In summary, the bear didn't move farther from station B after three days.