Question

Using satellite technology, the distance between two aircraft can be measured by keeping track of the angle between them and the distance of each plane to the tracking station.
Assume plane 1 is 176.27 miles away and plane 2 is 222.34 miles away and the angle formed with the tracking station is 38.59°. How far apart are the planes?

Answer 1

Looks like a direct application of the Law of Cosines.

Answer 2

so
i have this figure?

Answer 3

Yes, that's how I interpreted it as well.

Answer 4

im confused on how I would plug these into the formula

Answer 5

Good.

Answer 6

You can choose to place your known parts wherever you want. Then we can make the equation.

Answer 7

so i get \[C ^{2} = a^2 + b^2 -2abcosC\]
\[222.34^2 = 3859^2 + 176.27 -2(a)(176.27)(\cos(C)\]

Answer 8

where do i go from here?

Answer 9

It's not convenient to apply the law as you did there.

Answer 10

any suggestions?

Answer 11

Rather, if we're using the expression \[c^2=a^2+b^2-2ab\cos C,\] it is more convenient to let the unknown side be \(c\).

Answer 12

Then that will be our only unknown, since we automatically know \(a\), \(b\), and the angle \(C\).

Answer 13

Well i need to work this out myself

Answer 14

I need help with plugging this in...

Answer 15

\(176.27^2+222.34^2-2\cdot176.27\cdot222.34 \cdot \cos 38.59^\circ = c^2\)

Answer 16

What do you get for \(c\)? I made an arithmetic mistake in my last one so let me know what you get and I'll verify it.

Answer 17

(I'm getting around 138.70 miles after recalculating.)

Answer 18

yea i got 138.705

Answer 19

Great :)

Answer 20

I should have said 138.71 miles. Can't believe I just failed at rounding. :D