Question

two rangers at stations located 10 miles apart both see a camper distress signal in the distance the signal is at a compass bearing of 70 degrees from the north station and 40 degrees from the south station find the distance to the angle signal from south station to the nearest hundred

Answer 1

To find the distance to the angle signal from the south station, we can use the concept of vectors and trigonometry. By finding the angles between the points and using the Law of Cosines, we can determine the distance. In this case, the distance is approximately 12.247 miles when rounded to the nearest hundred.

Step-by-step explanation:

To find the distance to the angle signal from the south station, we can use the concept of vectors and trigonometry. Let's consider the two rangers as points A and B, with A being the north station and B being the south station. We are given that the signal is at a compass bearing of 70 degrees from point A and 40 degrees from point B.

First, we need to find the bearings of the signal with respect to the positive x-axis. The bearing from point A is 70 degrees, so the angle from the positive x-axis is 90 - 70 = 20 degrees. The bearing from point B is 40 degrees, so the angle from the positive x-axis is 180 + 40 = 220 degrees.

Answer 2

10 miles

Step-by-step explanation:

∠1 = 70° and ∠3 = 40°. Angles of a triangle add up to 180°, so ∠2 = 70°.

Using law of sines:

10 / sin(∠2) = x / sin(∠1)

10 / sin(70°) = x / sin(70°)

x = 10