anonymous
  • anonymous
Please Help with this Trig Question.. An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. If the distance from the observer (O) to the bird (B) is 15,000 ft., how far is the bird (B) from its nest (N)? Round to the nearest whole number.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Please help me
anonymous
  • anonymous
@welshfella
anonymous
  • anonymous
@AngusV

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anonymous
  • anonymous
@DarkMoonZ
anonymous
  • anonymous
@shenandoah123
anonymous
  • anonymous
|dw:1435695652832:dw|
anonymous
  • anonymous
Well, think about it - what trigonometric function do you know that can possibly use an angle and the OPPOSING side of that angle to tell you more about the hypotenuse in a right-angled triangle ? Make a guess.
anonymous
  • anonymous
Pythagorean theorem?
anonymous
  • anonymous
Not a bad idea, but to apply it means you'd have to know what the length of the other side is too, right ? Unfortunately, that you do not know. You have to use the angle and the opposing side only.
anonymous
  • anonymous
Can you explain in layman's terms im not grasping what you are saying. The lesson the teacher provided was terrible. I dont know this things.
anonymous
  • anonymous
Can you explain in layman's terms im not grasping what you are saying. The lesson the teacher provided was terrible. I dont know this things.
anonymous
  • anonymous
Alright. The basic trigonometric functions are sine, cosine, tan and cot. They are quite useful once you understand them because they have all sorts of interesting properties to them. Only - and only - in right angled triangles, they are defined so: 1) The sine of an angle = the opposing side of the angle / the hypotenuse 2) The cosine of an angle = the other side (non-opposing one) / the hypotenuse 3) The tangent of an angle = the opposing side of the angle / the other side of the angle 4) The cotangent of an angle = the other side of the angle / the opposing side of the angle Also, keep in mind that in math it is considered that if an angle is know then all of its trigonometric functions are also known. In other words, if you know that the angle is 55 degrees that means it is considered KNOWN what sine, cosine, tan and cotan of 55 degrees is. You can just pick up a calculator and plug it in yourself. There are also some key properties that link these 4 trigonometric functions all together: 1) sin(x) ^2 + cos(x)^2=1 2) tan(x)= sin(x)/cos(x) 3) cot(x)=cos(x)/sin(x) and so forth. For now we need only to focus on the first half of this.
anonymous
  • anonymous
Okay let me see if I can process all of this AFTER I understand what we're doing here lol
anonymous
  • anonymous
That's really all there is to it for now. You have the angle so you clearly know what sine,cosine,tan and cotan of that angle is (you will have to use a calculator for them) - all you need to do now is to look at the problem and figure out which of these trigonometric functions would be of use to you.
anonymous
  • anonymous
Okay Im trying to understand but Im still at point blank
anonymous
  • anonymous
Alright, here they also give you the opposing side of the angle of 55 degrees - that should instantly tell you that you should be using sine. Recall how sine is defined in a right angled triangle: sine= opposing side / hypotenuse So here, sine(55)= the opposing side (which here is 15 000 ft) / the hypotenuse (which here is the distance between the bird and the nest)
anonymous
  • anonymous
Okay. Im not sure what to say but okay..
anonymous
  • anonymous
Therefore, the hypotenuse = 15 000 ft / sin (55) and that's your answer - all you need to do is pick up a calculator and do sin(55) and then do that division.
anonymous
  • anonymous
Are serious thats all?
anonymous
  • anonymous
Yup.
anonymous
  • anonymous
Once you get it it becomes trivial.
anonymous
  • anonymous
My teacher made it so complex XD I need to switch to your class if you were a teacher
anonymous
  • anonymous
Haha, thank you. Well, it can get pretty complex to be honest, but it's pointless to get into that if you haven't mastered the basics first.
anonymous
  • anonymous
Thank you :)
anonymous
  • anonymous
The hardest part would be to make that drawing. I hate it when problems have too many words in them.
anonymous
  • anonymous
Yea Same it gets really confusing.
anonymous
  • anonymous
Here's a different example |dw:1435696718745:dw|
anonymous
  • anonymous
I got 18311.61883 but thats not one of my choices
anonymous
  • anonymous
Here for example you can't you sine because you don't know what the opposing side of the angle is - but you know what the length of the other side is so you use cosine. cos(30) = 10 / x so x = 10/ cos(30)
anonymous
  • anonymous
Angus I got 18311.61883 but thats not one of my choices
anonymous
  • anonymous
That surely means I must've drawn the thing wrong. It's the text that kills me, not the math.
anonymous
  • anonymous
Hold on let me upload this image
anonymous
  • anonymous
Alright, that would be best.
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Oh, well that changes things a bit.
anonymous
  • anonymous
My mistake for not uploading it earlier, I'm sorry lol.
anonymous
  • anonymous
Well, now they give you the angle and the hypotenuse and they're asking for the other side (non-opposing one) to the angle. Any ideas on what trigonometric function you should be using ?
anonymous
  • anonymous
Refer to the long text above.
anonymous
  • anonymous
Hmm, isnt cos the reverse of sine, so would it be cos?
anonymous
  • anonymous
Long answer: Well, you nailed it - but keep in mind that sine is not the exact reverse of cos - the inverse function of cos bears the name of arccos and it's a different business. But yeah, in a sense you could call it that way since it's defined as the other side / the hypotenuse instead of the opposing side / the hypotenuse. Short answer: yes.
anonymous
  • anonymous
Now, we have: cos(55) = x / 15 000 ft Therefore x= cos(55) * 15 000
anonymous
  • anonymous
Thank you so much let me check this out.
anonymous
  • anonymous
Take your time.
anonymous
  • anonymous
SUCCESS!
anonymous
  • anonymous
It comes out to 8603.646545, but rounded to the nearest whole number would be 8604; that would be correct?
anonymous
  • anonymous
Good job ! The exercises will test your ability to identify which proper function you should use - tan and cotan might be confusing at first but they're pretty much the same thing. Yes - if rounded to the nearest whole number. Angles tend to have long non-repeating digits when you apply trigonometric functions to them unless they're nice values (30,45,60,90,180 so forth).
anonymous
  • anonymous
If I need you help again do I just @AngusV ?
anonymous
  • anonymous
For instance, sin(30) is 1/2 basically. What that tells you is that no matter how big your triangle / roof / whatever is, if you make a 30 degrees angle like this |dw:1435697604538:dw| The opposing side to that angle will always be HALF of the hypotenuse.
anonymous
  • anonymous
Sure thing if you catch me around. I have to go for now but yeah, no problem.
anonymous
  • anonymous
|dw:1435697676956:dw|
anonymous
  • anonymous
You're welcome !
anonymous
  • anonymous
That art deserves recognition lol
anonymous
  • anonymous
See ya around Angus!

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