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.

- anonymous

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- anonymous

Please help me

- anonymous

- anonymous

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## More answers

- anonymous

- anonymous

- anonymous

|dw:1435695652832:dw|

- 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

Pythagorean theorem?

- 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

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

Okay let me see if I can process all of this AFTER I understand what we're doing here lol

- 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

Okay Im trying to understand but Im still at point blank

- 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

Okay. Im not sure what to say but okay..

- 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

Are serious thats all?

- anonymous

Yup.

- anonymous

Once you get it it becomes trivial.

- anonymous

My teacher made it so complex XD I need to switch to your class if you were a teacher

- 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

Thank you :)

- anonymous

The hardest part would be to make that drawing. I hate it when problems have too many words in them.

- anonymous

Yea Same it gets really confusing.

- anonymous

Here's a different example
|dw:1435696718745:dw|

- anonymous

I got 18311.61883 but thats not one of my choices

- 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

Angus I got 18311.61883 but thats not one of my choices

- anonymous

That surely means I must've drawn the thing wrong. It's the text that kills me, not the math.

- anonymous

Hold on let me upload this image

- anonymous

Alright, that would be best.

- anonymous

##### 1 Attachment

- anonymous

Oh, well that changes things a bit.

- anonymous

My mistake for not uploading it earlier, I'm sorry lol.

- 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

Refer to the long text above.

- anonymous

Hmm, isnt cos the reverse of sine, so would it be cos?

- 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

Now, we have:
cos(55) = x / 15 000 ft
Therefore
x= cos(55) * 15 000

- anonymous

Thank you so much let me check this out.

- anonymous

Take your time.

- anonymous

SUCCESS!

- anonymous

It comes out to 8603.646545, but rounded to the nearest whole number would be 8604; that would be correct?

- 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

If I need you help again do I just @AngusV ?

- 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

Sure thing if you catch me around. I have to go for now but yeah, no problem.

- anonymous

|dw:1435697676956:dw|

- anonymous

You're welcome !

- anonymous

That art deserves recognition lol

- anonymous

See ya around Angus!

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