applied trigonometry question!! (1 Viewer)

[scilove]

I've been stuck on this question for a while and i can't seem to get it because i cant find the angle of the flag pole to the horizontal, or maybe im not drawing it right.

P,A,B,C are four points in order on a straight road that runs up a hillside and makes a constant angle of 10 degrees with the horizontal. A flagpole whose height is h meters stands at P. From A and B, the top of the flagpole has elevations of 30 degrees and 5 degrees respectively above the horizontal. If AB is 100m long, what is the height of the flagpole?
If BC is also 100m long, what is the elevation of the top of the flagpole from C?

The question is from the 2u and 3u fitzpatrick book under applied trigonometry question 2.

Thanks in advance!! these questions are usually straight forward but i idk what im doing here.

 

[Drongoski]

This question (Ex 21(a), Q2 - old Fitzpatrick, 3U book) is not very straightforward.

I had 39.9727 . . . m for h and -0.9416 deg for angle of elevation (i.e. 56.49' angle of depression). Since the question asked fot the angle of elevation, I thought my answer was incorrect, until I located the question and know I'm correct.

How to explain to you? It's very hard without being able to show you the diagram.

But let x be distance PA and we have a series of equations:



Use the compound angle formula to expand sin(100 - theta)

I finally solved for: cot(theta) = 6.177056963/sin 100

 

[scilove]

This question (Ex 21(a), Q2 - old Fitzpatrick, 3U book) is not very straightforward.

I had 39.9727 . . . m for h and -0.9416 deg for angle of elevation (i.e. 56.49' angle of depression). Since the question asked fot the angle of elevation, I thought my answer was incorrect, until I located the question and know I'm correct.

How to explain to you? It's very hard without being able to show you the diagram.

But let x be distance PA and we have a series of equations:



Use the compound angle formula to expand sin(100 - theta)

thank you replying but could you please explain how you got the angles like 60 and 40?
my triangle thats in A-B has angles 5,150 and 25

 

[Drongoski]

thank you replying but could you please explain how you got the angles like 60 and 40?
my triangle thats in A-B has angles 5,150 and 25

Flagpole is vertical (perpendicular to the horizontal)

40 = 10 + 30 and 25 = 15 + 10

triangle with vertex A has 3 angles: 40, 80, 60

triangle with vertex B has angles: 80, 15, 85

triangle with vertex C has angles: 80, theta, 100 - theta

The flagpole constitutes the left side of each triangle.

 

[pikachu975]

thank you replying but could you please explain how you got the angles like 60 and 40?
my triangle thats in A-B has angles 5,150 and 25

What's the answer in the back of book?

I got 10.31m for height of the flagpole, if it's right I'll post the working if not then nvm.

 

[Drongoski]

I have already posted the correct answer. h = 39.97 m

 

[scilove]

What's the answer in the back of book?

I got 10.31m for height of the flagpole, if it's right I'll post the working if not then nvm.

i got the same as you, but drongoski got the answer right

 

[scilove]

Flagpole is vertical (perpendicular to the horizontal)

40 = 10 + 30 and 25 = 15 + 10.

how can you add the 30 and the 10 if they're in completely different places?
ive got the pole and the horizontal perpendicular but, I have a slanted line between them that has angle A with 30 degrees,B with 5 degrees , and angle C. then the angle 10 is between the horizontal and the slanted line. so i don't see how you could add them.

 

[pikachu975]

how can you add the 30 and the 10 if they're in completely different places?
ive got the pole and the horizontal perpendicular but, I have a slanted line between them that has angle A with 30 degrees,B with 5 degrees , and angle C. then the angle 10 is between the horizontal and the slanted line. so i don't see how you could add them.

Yeah idk how you can add them, they're in different planes of the 3d plane so idk how that works.

 

[Drongoski]

how can you add the 30 and the 10 if they're in completely different places?
ive got the pole and the horizontal perpendicular but, I have a slanted line between them that has angle A with 30 degrees,B with 5 degrees , and angle C. then the angle 10 is between the horizontal and the slanted line. so i don't see how you could add them.

P, A, B and C are on a straight line (along a straight road).

 

[Drongoski]

Yeah idk how you can add them, they're in different planes of the 3d plane so idk how that works.

Draw a long horizontal line and then a straight line with inclination of 10 degrees above the horizontal. Place 4 points: P, A, B and C up this inclined line, with distances PA = x (unknown), AB = 100, BC = 100. Angle of elevation 0f 30 deg from A means the line of sight from A to the top of the flag pole makes an angle of 40 deg (30 + 10) with the inclined line. etc etc.

 

[pikachu975]

Draw a long horizontal line and then a straight line with inclination of 10 degrees above the horizontal. Place 4 points: P, A, B and C up this inclined line, with an distances PA = x (unknown), AB = 100, BC = 100. Angle of elevation 0f 30 deg from A means the line of sight from A to the top of the flag pole makes an angle of 40 deg (30 + 10) with the inclined line. etc etc.

Can you please upload a drawing to imgur if you can?

 

[Drongoski]

Can you please upload a drawing to imgur if you can?

Embarrassingly I don't know how. Else it'd be so much easier as I can then simply take a picture of my written solution and upload it. Hence my tortured descriptions. I'm so sorry.

But you should be able to put together the pieces I have already posted.

 

[pikachu975]

Embarrassingly I don't know how. Else it'd be so much easier as I can then simply take a picture of my written solution and upload it. Hence my tortured descriptions. I'm so sorry.

But you should be able to put together the pieces I have already posted.

Take a photo with phone/ipad then go on the imgur website/app and click upload, choose a photo then post the link here.

 

[scilove]

okay so this is what my diagram looks like
http://i.imgur.com/hAuUM0c.jpg

 

[pikachu975]

okay so this is what my diagram looks like
http://i.imgur.com/hAuUM0c.jpg

Exactly same as mine which is why I don't get why you can add the 10.

 

[He-Mann]

Exactly same as mine which is why I don't get why you can add the 10.

The diagram is wrong because you labelled the angle of elevation at A and B incorrectly.

 

[pikachu975]

The diagram is wrong because you labelled the angle of elevation at A and B incorrectly.

Oh where is it? I just assumed it was there because I thought it was 3D trig.

 

[He-Mann]

Oh where is it? I just assumed it was there because I thought it was 3D trig.

Why is this 3D trig?

Looking at the diagram scilove drew, I can see why you may think this is 3D by your perception. Maybe read the question again.

Observing scilove's diagram from a 2D perspective, i.e. from a side-view of the hill, draw a horizontal line at point A. The angle from this horizontal line to the line from A to the apex of the flagpole is 30 degrees.

The angle where she labelled it as 30 degrees should be 40 degrees (by geometry and the above). Do the same thing for point B.

 

[scilove]

Looking at the diagram scilove drew, I can see why you may think this is 3D by your perception. Maybe read the question again.

You're completely right thank you so much!
http://imgur.com/7iFyYNK ( i know it's messy but hey it worked!!)

now that i drew the diagram and read the question again i can see that it said 'above the horizon' -- i completely missed that.