bearing questions?

Question

two game wardens are known to be 1.5 miles apart and both observe a bear. the bear is N 22.5 degrees E of warden wain and N 28.8 degrees W of warden ryan. how far is each warden from the bear?

i think youre supposed to use law of sines or law of cosines to solve.

Answer 1

I don't think there's enough information there. There is a line of bearing between the bear and each ranger; and the rangers are known to be 1.5 miles apart.

However, if either of the rangers is standing right next to the bear, then the other will be right at 1.5 miles away; and vice versa. Without some additional information (one of the ranger's distances, the bearing between the two rangers, something else to clarify the relationship between the three positions), you can't say how far the rangers are except that one is southwest and the other southeast.

Good luck!

Answer 2

This problem is indeterminate unless we know the direction from one warden to the other. Make a dot on a piece of paper, label it bear. Draw a line through it on the N 22.5° E heading, and another line through it on the N 28.8° W heading. Warden Wain is somewhere south on the NE line, warden ryan is somewhere south on the NW line. But wain could be 20 ft from the bear, which would put ryan just short of 1.5 miles away on his line, or ryan could be 20 ft from the bear, which would put wain almost 1.5 miles away down his line. Or they could be equal distances down their respective lines, a distance sufficient to put 1.5 miles between them.

If you assume wain is exactly due west of ryan, then you can solve for the distance each is from the bear using law of sines. Angle at the top of the triangle is 180 - 67.5 - 61.2 = 51.3°. Let wain's distance be w, ryan's r. Then

1.5 / sin 51.3 = w / sin 61.2 = r / sin 67.5, and

w = 1.5 sin 61.2 / sin 51.3 = 1.68 mi.
r = 1.5 sin 67.5 / sin 51.3 = 1.78 mi.