Assume two radar stations which are 39 miles apart are both tracking a plane. At a given moment, the angle between station 1 and the plane is 59.83°, while the angle between station 2 and the plane is 55.54°. With this information, how far is the plane from station 2?

Guest Apr 16, 2020

#1**+1 **

Question is unclear, but Here is a solution using law of sines: (there is a better answer below from arism)

ElectricPavlov Apr 16, 2020

#3**0 **

This solution and the one I posted are both plausible as the question is not specific enough to discern which one is the correct answer, but this question's distance gives reason that the altitude of the plane is well over 2,000,000, which is just impossible. This is correct mathematically, but reasonably this is impossible and incorrect

arism
Apr 16, 2020

#4**0 **

I think your answer is better BUT:

I am not sure where you arrived at a dimensionless 2,000,000!

When questions are unclear.....so are the resuts, huh?

ElectricPavlov
Apr 16, 2020

#6**0 **

**EP, your solution is proof you are staying inside the obtuse scalene triangle, while thinking outside of the box.**

The (2,000,000) Arism comments on is the elevation (in feet) above ground level; this works out to about 379 statute miles or 329 nautical miles. **The actual elevation for your equation is 371.64 statute miles or 322.95 nautical miles**.

GA

GingerAle
Apr 17, 2020

#2**0 **

Let's set up a triangle for this equation

lines intersect here, this point is the plane

/\

65.22

/ \

/59.38_________________55.4\

39 miles

Since the angle of the plane in relation to the two stations is 65.22, we can set up a law of wines.

\({39\over \sin(65.22)} = {x \over \sin 59.38}\)

x is the distance between the plane and station 2. We now cross multiply and we find the answer.

\(x = {39\sin(59.38)\over\sin(65.22)} \approx 17.4\)

The distance between station 2 and the plane is about 17.4 miles

arism Apr 16, 2020

#5**0 **

Arism, the ** law of wines **(red, white, and blush) is a great law, but it apparently returns the wrong answer here. You have several mistakes in your solution. The angle of intersection at the plane has to be 64.63° for a non-obtuse triangle. Also, the sine function calculation was set for radian measure, which returned an erroneous 17.4.

After downing some red, white, and blush, and correcting for these errors, the distance to tower #2 is 37.3 miles. The elevation is 30.77 statute miles. This also *is correct mathematically, but reasonably this is impossible and incorrect*... This is 7.38 statute miles higher than the (dubious) record of 23.39 statute miles for a jet aircraft.

** No matter which assumption (EP's or yours), the elevation is well above physical limits of an atmospheric-engine-powered aircraft.**

GA

GingerAle
Apr 17, 2020