Trig/Precalculus help! Airplane bearing and distance from mountain

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A plane flying a straight course observes a mountain at a bearing of 35.1degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time​ later, the bearing to the mountain becomes 45.1degrees. How far is the plane from the mountain when the second bearing is taken​ (to the nearest tenth of a​ km)?

I'm unsure of how to make a drawing of this problem.

trigonometry

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asked Jul 25 at 0:32

Mia Nguyen

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A plane flying a straight course observes a mountain at a bearing of 35.1degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time​ later, the bearing to the mountain becomes 45.1degrees. How far is the plane from the mountain when the second bearing is taken​ (to the nearest tenth of a​ km)?

I'm unsure of how to make a drawing of this problem.

trigonometry

share|cite|improve this question

asked Jul 25 at 0:32

Mia Nguyen

1

add a comment | 

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

A plane flying a straight course observes a mountain at a bearing of 35.1degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time​ later, the bearing to the mountain becomes 45.1degrees. How far is the plane from the mountain when the second bearing is taken​ (to the nearest tenth of a​ km)?

I'm unsure of how to make a drawing of this problem.

trigonometry

share|cite|improve this question

asked Jul 25 at 0:32

Mia Nguyen

1

A plane flying a straight course observes a mountain at a bearing of 35.1degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time​ later, the bearing to the mountain becomes 45.1degrees. How far is the plane from the mountain when the second bearing is taken​ (to the nearest tenth of a​ km)?

I'm unsure of how to make a drawing of this problem.

trigonometry

share|cite|improve this question

asked Jul 25 at 0:32

Mia Nguyen

1

share|cite|improve this question

share|cite|improve this question

asked Jul 25 at 0:32

Mia Nguyen

1

asked Jul 25 at 0:32

Mia Nguyen

1

asked Jul 25 at 0:32

Mia Nguyen

1

1

add a comment | 

add a comment | 

3 Answers
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up vote
2
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In the diagram below, $I$ is the point where the initial bearing is taken, $N$ is the point where the new bearing is taken, and $M$ is the position of the mountain. The arrow indicates the direction of the plane. Note that the angles measure the direction to the mountain relative to the course of the plane.

Your task is to use the given information to find $|NM|$, the distance from the point where the second bearing is taken to the mountain.

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answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

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Hint: Draw a ray $OA$ of length $9$ and angle $35.1^circ$ Then draw another ray $AB$ with new angle $45.1 ^circ$. Then you will have ray $OB$ that will indicate the distance with the new bearing. Your job will then be to find the other angles and the actual distance.

share|cite|improve this answer

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for catching this...I've edited my post above.
  – bjcolby15
  Jul 25 at 10:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
  – N. F. Taussig
  Jul 25 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
  – bjcolby15
  Jul 25 at 11:56
  

  
  
  
  

add a comment | 

up vote
0
down vote

It's easy to see that angle MNI is $180-45.1=134.9$ degrees. So using law of cuisines on triangle MNI we get
$(sin 134.9)/9=(sin 35.1)/x$. We can approximate the angles as $135$ and $35$ and using the sine addition formula to find that $x$ is approximately $9sqrt2sin 35$ which is about $7.3$.

share|cite|improve this answer

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

add a comment | 

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

In the diagram below, $I$ is the point where the initial bearing is taken, $N$ is the point where the new bearing is taken, and $M$ is the position of the mountain. The arrow indicates the direction of the plane. Note that the angles measure the direction to the mountain relative to the course of the plane.

Your task is to use the given information to find $|NM|$, the distance from the point where the second bearing is taken to the mountain.

share|cite|improve this answer

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

add a comment | 

up vote
2
down vote

In the diagram below, $I$ is the point where the initial bearing is taken, $N$ is the point where the new bearing is taken, and $M$ is the position of the mountain. The arrow indicates the direction of the plane. Note that the angles measure the direction to the mountain relative to the course of the plane.

Your task is to use the given information to find $|NM|$, the distance from the point where the second bearing is taken to the mountain.

share|cite|improve this answer

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

add a comment | 

up vote
2
down vote

up vote
2
down vote

In the diagram below, $I$ is the point where the initial bearing is taken, $N$ is the point where the new bearing is taken, and $M$ is the position of the mountain. The arrow indicates the direction of the plane. Note that the angles measure the direction to the mountain relative to the course of the plane.

Your task is to use the given information to find $|NM|$, the distance from the point where the second bearing is taken to the mountain.

share|cite|improve this answer

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

In the diagram below, $I$ is the point where the initial bearing is taken, $N$ is the point where the new bearing is taken, and $M$ is the position of the mountain. The arrow indicates the direction of the plane. Note that the angles measure the direction to the mountain relative to the course of the plane.

Your task is to use the given information to find $|NM|$, the distance from the point where the second bearing is taken to the mountain.

share|cite|improve this answer

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

share|cite|improve this answer

share|cite|improve this answer

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

answered Jul 25 at 11:08

N. F. Taussig

38.2k93053

38.2k93053

add a comment | 

add a comment | 

up vote
0
down vote

Hint: Draw a ray $OA$ of length $9$ and angle $35.1^circ$ Then draw another ray $AB$ with new angle $45.1 ^circ$. Then you will have ray $OB$ that will indicate the distance with the new bearing. Your job will then be to find the other angles and the actual distance.

share|cite|improve this answer

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for catching this...I've edited my post above.
  – bjcolby15
  Jul 25 at 10:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
  – N. F. Taussig
  Jul 25 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
  – bjcolby15
  Jul 25 at 11:56
  

  
  
  
  

add a comment | 

up vote
0
down vote

Hint: Draw a ray $OA$ of length $9$ and angle $35.1^circ$ Then draw another ray $AB$ with new angle $45.1 ^circ$. Then you will have ray $OB$ that will indicate the distance with the new bearing. Your job will then be to find the other angles and the actual distance.

share|cite|improve this answer

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for catching this...I've edited my post above.
  – bjcolby15
  Jul 25 at 10:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
  – N. F. Taussig
  Jul 25 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
  – bjcolby15
  Jul 25 at 11:56
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

Hint: Draw a ray $OA$ of length $9$ and angle $35.1^circ$ Then draw another ray $AB$ with new angle $45.1 ^circ$. Then you will have ray $OB$ that will indicate the distance with the new bearing. Your job will then be to find the other angles and the actual distance.

share|cite|improve this answer

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

Hint: Draw a ray $OA$ of length $9$ and angle $35.1^circ$ Then draw another ray $AB$ with new angle $45.1 ^circ$. Then you will have ray $OB$ that will indicate the distance with the new bearing. Your job will then be to find the other angles and the actual distance.

share|cite|improve this answer

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

share|cite|improve this answer

share|cite|improve this answer

edited Jul 25 at 11:51

edited Jul 25 at 11:51

edited Jul 25 at 11:51

answered Jul 25 at 1:04

bjcolby15

7921616

answered Jul 25 at 1:04

bjcolby15

7921616

answered Jul 25 at 1:04

bjcolby15

7921616

7921616

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for catching this...I've edited my post above.
  – bjcolby15
  Jul 25 at 10:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
  – N. F. Taussig
  Jul 25 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
  – bjcolby15
  Jul 25 at 11:56
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for catching this...I've edited my post above.
  – bjcolby15
  Jul 25 at 10:17
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
  – N. F. Taussig
  Jul 25 at 10:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
  – bjcolby15
  Jul 25 at 11:56
  

  
  
  
  

Thanks for catching this...I've edited my post above.
– bjcolby15
Jul 25 at 10:17

Thanks for catching this...I've edited my post above.
– bjcolby15
Jul 25 at 10:17

1

1

In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
– N. F. Taussig
Jul 25 at 10:20

In your new formulation, the mountain is at $O$, the first bearing is taken at $A$, and the second bearing is taken at $B$, so we want to find $OB$, the distance between the point where the second bearing is taken and the mountain.
– N. F. Taussig
Jul 25 at 10:20

Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
– bjcolby15
Jul 25 at 11:56

Can you tell I've been out of the geometry business for awhile (or I hadn't had my breakfast?) XD You have a better explanation and a better answer below.
– bjcolby15
Jul 25 at 11:56

add a comment | 

up vote
0
down vote

It's easy to see that angle MNI is $180-45.1=134.9$ degrees. So using law of cuisines on triangle MNI we get
$(sin 134.9)/9=(sin 35.1)/x$. We can approximate the angles as $135$ and $35$ and using the sine addition formula to find that $x$ is approximately $9sqrt2sin 35$ which is about $7.3$.

share|cite|improve this answer

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

add a comment | 

up vote
0
down vote

It's easy to see that angle MNI is $180-45.1=134.9$ degrees. So using law of cuisines on triangle MNI we get
$(sin 134.9)/9=(sin 35.1)/x$. We can approximate the angles as $135$ and $35$ and using the sine addition formula to find that $x$ is approximately $9sqrt2sin 35$ which is about $7.3$.

share|cite|improve this answer

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

add a comment | 

up vote
0
down vote

up vote
0
down vote

It's easy to see that angle MNI is $180-45.1=134.9$ degrees. So using law of cuisines on triangle MNI we get
$(sin 134.9)/9=(sin 35.1)/x$. We can approximate the angles as $135$ and $35$ and using the sine addition formula to find that $x$ is approximately $9sqrt2sin 35$ which is about $7.3$.

share|cite|improve this answer

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

It's easy to see that angle MNI is $180-45.1=134.9$ degrees. So using law of cuisines on triangle MNI we get
$(sin 134.9)/9=(sin 35.1)/x$. We can approximate the angles as $135$ and $35$ and using the sine addition formula to find that $x$ is approximately $9sqrt2sin 35$ which is about $7.3$.

share|cite|improve this answer

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

share|cite|improve this answer

share|cite|improve this answer

edited Jul 25 at 13:40

edited Jul 25 at 13:40

edited Jul 25 at 13:40

answered Jul 25 at 13:21

Shrey Joshi

1389

answered Jul 25 at 13:21

Shrey Joshi

1389

answered Jul 25 at 13:21

Shrey Joshi

1389

1389

add a comment | 

add a comment | 

 

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