Distance Between Two Airplanes [closed]

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Two small airplanes leave the Calgary airport at the
same time. The first flies at $225$km/h at a heading of $320^circ$,
while the second flies at $190$km/h at a heading of $70^circ$. How far
apart are they after $2$ hours?

How should I proceed?

algebra-precalculus trigonometry

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edited Jul 26 at 17:02

Math Lover

12.3k21232

asked Jul 26 at 16:42

Bill

596

closed as off-topic by Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne Jul 27 at 4:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
  – fleablood
  Jul 26 at 16:45
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
  – NickD
  Jul 26 at 16:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
  – Doug M
  Jul 26 at 17:13
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
  – NickD
  Jul 26 at 18:44
  

  
  
  
  

add a comment | 

up vote
-2
down vote

favorite

Two small airplanes leave the Calgary airport at the
same time. The first flies at $225$km/h at a heading of $320^circ$,
while the second flies at $190$km/h at a heading of $70^circ$. How far
apart are they after $2$ hours?

How should I proceed?

algebra-precalculus trigonometry

share|cite|improve this question

edited Jul 26 at 17:02

Math Lover

12.3k21232

asked Jul 26 at 16:42

Bill

596

closed as off-topic by Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne Jul 27 at 4:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
  – fleablood
  Jul 26 at 16:45
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
  – NickD
  Jul 26 at 16:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
  – Doug M
  Jul 26 at 17:13
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
  – NickD
  Jul 26 at 18:44
  

  
  
  
  

add a comment | 

up vote
-2
down vote

favorite

up vote
-2
down vote

favorite

Two small airplanes leave the Calgary airport at the
same time. The first flies at $225$km/h at a heading of $320^circ$,
while the second flies at $190$km/h at a heading of $70^circ$. How far
apart are they after $2$ hours?

How should I proceed?

algebra-precalculus trigonometry

share|cite|improve this question

edited Jul 26 at 17:02

Math Lover

12.3k21232

asked Jul 26 at 16:42

Bill

596

Two small airplanes leave the Calgary airport at the
same time. The first flies at $225$km/h at a heading of $320^circ$,
while the second flies at $190$km/h at a heading of $70^circ$. How far
apart are they after $2$ hours?

How should I proceed?

algebra-precalculus trigonometry

share|cite|improve this question

edited Jul 26 at 17:02

Math Lover

12.3k21232

asked Jul 26 at 16:42

Bill

596

share|cite|improve this question

share|cite|improve this question

edited Jul 26 at 17:02

Math Lover

12.3k21232

edited Jul 26 at 17:02

Math Lover

12.3k21232

edited Jul 26 at 17:02

Math Lover

12.3k21232

12.3k21232

asked Jul 26 at 16:42

Bill

596

asked Jul 26 at 16:42

Bill

596

asked Jul 26 at 16:42

Bill

596

596

closed as off-topic by Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne Jul 27 at 4:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne Jul 27 at 4:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Math Lover, amWhy, Adrian Keister, Taroccoesbrocco, Isaac Browne

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
  – fleablood
  Jul 26 at 16:45
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
  – NickD
  Jul 26 at 16:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
  – Doug M
  Jul 26 at 17:13
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
  – NickD
  Jul 26 at 18:44
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
  – fleablood
  Jul 26 at 16:45
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
  – NickD
  Jul 26 at 16:47
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
  – Doug M
  Jul 26 at 17:13
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
  – NickD
  Jul 26 at 18:44
  

  
  
  
  

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
– fleablood
Jul 26 at 16:45

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula. Or the law of cosines.
– fleablood
Jul 26 at 16:45

I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
– NickD
Jul 26 at 16:47

I presume you can assume that all this happens on a Euclidean plane and does not have to take into account the curvature of the Earth. If so, you are given the two sides of a triangle and the angle between them: you have to find the third side.
– NickD
Jul 26 at 16:47

1

1

@NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
– Doug M
Jul 26 at 17:13

@NickD at the scales relevant to this problem the impact of curvature of the earth is < 15 meters. Which is a smaller consideration that other fudges such as can two planes really take off from the same runway at the same time.
– Doug M
Jul 26 at 17:13

1

1

I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
– NickD
Jul 26 at 18:44

I know, but I was just making sure that it was not an exercise in spherical trigonometry, where different formulas should be used.
– NickD
Jul 26 at 18:44

add a comment | 

1 Answer
1

active

oldest

votes

up vote
0
down vote



accepted

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*cos 320, 2*225*sin 320)$ and the other will be and $(2*190*cos 70, 2*190*sin 70)$.

Their distance will be $sqrt (2*225cos 320 - 2*190cos 70)^2 +(2*225sin 320 - 2*190sin 70)^2$

.....

Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*cos (320 - 70)$.

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote



accepted

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*cos 320, 2*225*sin 320)$ and the other will be and $(2*190*cos 70, 2*190*sin 70)$.

Their distance will be $sqrt (2*225cos 320 - 2*190cos 70)^2 +(2*225sin 320 - 2*190sin 70)^2$

.....

Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*cos (320 - 70)$.

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

add a comment | 

up vote
0
down vote



accepted

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*cos 320, 2*225*sin 320)$ and the other will be and $(2*190*cos 70, 2*190*sin 70)$.

Their distance will be $sqrt (2*225cos 320 - 2*190cos 70)^2 +(2*225sin 320 - 2*190sin 70)^2$

.....

Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*cos (320 - 70)$.

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

add a comment | 

up vote
0
down vote



accepted

up vote
0
down vote



accepted

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*cos 320, 2*225*sin 320)$ and the other will be and $(2*190*cos 70, 2*190*sin 70)$.

Their distance will be $sqrt (2*225cos 320 - 2*190cos 70)^2 +(2*225sin 320 - 2*190sin 70)^2$

.....

Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*cos (320 - 70)$.

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*cos 320, 2*225*sin 320)$ and the other will be and $(2*190*cos 70, 2*190*sin 70)$.

Their distance will be $sqrt (2*225cos 320 - 2*190cos 70)^2 +(2*225sin 320 - 2*190sin 70)^2$

.....

Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*cos (320 - 70)$.

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

share|cite|improve this answer

share|cite|improve this answer

answered Jul 26 at 16:48

fleablood

60.3k22575

answered Jul 26 at 16:48

fleablood

60.3k22575

answered Jul 26 at 16:48

fleablood

60.3k22575

60.3k22575

add a comment | 

add a comment |