How to Graph the Horizontal Distance of a Jet from a House Using Trigonometry?

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Homework Help Overview

The discussion revolves around a trigonometric problem involving the angle of elevation from the top of a house to a jet flying above it. The original poster seeks to express the horizontal distance of the jet from the house in terms of a trigonometric function and to graph this function for a specified range of angles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the setup of a right triangle involving the angle of elevation, the horizontal distance, and the height of the jet. Questions arise about identifying the opposite and adjacent sides related to the angle x, as well as the appropriate trigonometric function to use.

Discussion Status

Participants are actively engaging in identifying the relationship between the sides of the triangle and the angle x. Some guidance has been offered regarding the use of the tangent function, and there is a progression towards expressing the horizontal distance in terms of trigonometric functions. However, there is still uncertainty and a lack of consensus on the next steps for graphing the function.

Contextual Notes

There are indications of confusion regarding the drawing of the triangle and the labeling of its sides. The original poster expresses feelings of frustration and helplessness, suggesting that they may be struggling with the foundational concepts of trigonometry.

lilchicadees
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The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizontal distance, in miles, of the jet from the house, express d in terms of a trigonometric function of x. The graph the function for 0< x <pi.
 
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Did you draw a right triangle involving x, d and 2 miles? That's a good place to start.
 
yes I did, now what?
 
From your triangle with d, x, and 2 labeled can you think of a trig function that involves them?
 
no, that's why I am asking...
 
ok, this is what I need to figure out. tan x=opp/adj = ?/?
 
lilchicadees said:
ok, this is what I need to figure out. tan x=opp/adj = ?/?

Very much so. Skip the last = ?/?. Just substitute the values for opp and adj.
 
well if I knew what they were I could..lol
 
maybe this graph will help..
 

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  • #10
lilchicadees said:
well if I knew what they were I could..lol

I'm starting to feel helpless here. You drew the picture, right? It should be right in front of you. Which is the adjacent side and which is the opposite side to the angle x?
 
  • #11
lilchicadees said:
maybe this graph will help..

How can you not know with such a gorgeous picture to help? Which leg is opposite the angle x and which is adjacent?
 
  • #12
the 2 mile side would be the opposite and the other would be the adjacent side.
 
  • #13
I have never done this before, so that is why I am lost...No I didnt draw the picture. It is supposed to help me.
 
  • #14
lilchicadees said:
the 2 mile side would be the opposite and the other would be the adjacent side.

Yes, so tan(x)=... just fill it in.
 
  • #15
tan(x)=2/? Grrrrrr
 
  • #16
lilchicadees said:
the 2 mile side would be the opposite and the other would be the adjacent side.

No offense, but this is getting to be like pulling teeth. The 'other' i.e. the 'adjacent side' is clearly labelled in your picture. It has a letter on it.
 
  • #17
tax(x)=2/d
 
  • #18
I do understand your frustration with me, just think how I feel.. :(
 
  • #19
I was wondering why do I need to forget the ?/?...
 
  • #20
lilchicadees said:
I was wondering why do I need to forget the ?/?...

I just meant you should fill in the ??'s. tan(x)=2/d is exactly what you want. You are basically done. Now just solve for d.
 
  • #21
I truly don't know how to solve for d. I must sound pretty stupid, huh?
 
  • #22
ok wait, is it d=2cot(x) ?
 
  • #23
oops, I mean 2/tan(x)
 
  • #24
lilchicadees said:
ok wait, is it d=2cot(x) ?

Sure. That's more than brilliant. I was hoping for just d=2/tan(x). But that's the same if not better.
 
  • #25
lilchicadees said:
oops, I mean 2/tan(x)

2/tan(x)=2*cot(x).
 
  • #26
ok, now I need to use this information to fill out that graph. How would I go about that?
 
  • #27
lilchicadees said:
ok, now I need to use this information to fill out that graph. How would I go about that?

You could start by plotting some points.
 

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