anonymous
  • anonymous
Anyone care to help me out with this easy problem? "Find sin, cos and tan of a triangle with area :0,465 m^2 side 1: 0,74 cm side 2: 0,0936 cm" Any ideas? How should I go about figuring out the answer? Thanks in advance!
Mathematics
chestercat
  • chestercat
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inkyvoyd
  • inkyvoyd
1/2 sin(included angle)* (AB)=area of triangle
anonymous
  • anonymous
Care to explain? :)
inkyvoyd
  • inkyvoyd
1/2 sin(angle between 1 and 2)*0,74*0,0936=0,465 solve for sin(angle between 1 and 2)

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inkyvoyd
  • inkyvoyd
btw, there are 3 angles in a triangle, and you have not specfied which angle you want the sin cos and tangent of. I'm assuming it is the angle made by sides 1 and 2.
inkyvoyd
  • inkyvoyd
the identity I have used is just the area formula for a triangle, which is 1/2 sin(included angle)*(ab)=area of triangle, where a and b are side lengths, and the included angle is the angle between a and b. To find cos x simply use sqrt(1-sin x) (pythagorean identity), and to find tan x simply use sin x/cos x
anonymous
  • anonymous
Hmm,.. Think you could walk me through each step and explain more thoroughly? :/ Not sure I understand your reasoning.
inkyvoyd
  • inkyvoyd
I am using the following formula as an identity: http://www.analyzemath.com/Geometry_calculators/area_triangle_sine.html
inkyvoyd
  • inkyvoyd
look at the bottom of this site for a proof http://www.mathopenref.com/triangleareasas.html
anonymous
  • anonymous
Ah, I think I understand! I'll get back to you if any additional questions arise. You rock.
inkyvoyd
  • inkyvoyd
good luck! you might want to show a quick proof of the formula if you need to show work for the problem. The area formula with SAS is common but I don't think it's required as standard curriculum (it's very useful though)
anonymous
  • anonymous
1.) shouldn't you start off by converting the sides from centimeters to meters? 2.) I understand the proof and everything, but what do I do when I have the value for sin(angle between a and b)?
inkyvoyd
  • inkyvoyd
Well, that sine was what you were looking for, right? you were asked to find the sin of the angle, and I'm assuming they wanted the sine of the included angle.
inkyvoyd
  • inkyvoyd
And yes, I did not catch that - you would need to convert units (which I didnot do correctly)
anonymous
  • anonymous
But what the cos and tan? How do I go about finding them?
anonymous
  • anonymous
What about*
anonymous
  • anonymous
Tried everything, can't figure it out. :/
inkyvoyd
  • inkyvoyd
sin^2 x+cos^2 x=1 sin x/cos x=tan x use the folowing identities. First use the first one to find cos x, the second after you found cos x to find tan x.
anonymous
  • anonymous
Think you could explain more in depth? :/
inkyvoyd
  • inkyvoyd
have you heard of the identity sin^2 x+cos ^2 x=1?
anonymous
  • anonymous
No, never, I'm afraid.
inkyvoyd
  • inkyvoyd
I might be being a bit too advanced then o.o
anonymous
  • anonymous
Yes, bring it down to my level. :)
anonymous
  • anonymous
10th grade precalc.
inkyvoyd
  • inkyvoyd
are you just getting introduced to trig fnctions? is this some online course in which you may be expected to know prereqs in trig that you have a knowledge gap in? Please answer these questions - the identities I'm using while valid might make your teacher angry etc
anonymous
  • anonymous
I'm kust starting to with trigonometric ratios and the like. Just need to know how to attain tan and cos from here.
inkyvoyd
  • inkyvoyd
Okay. Is this a right triangle?
anonymous
  • anonymous
Just started with trigonometric ratios*
anonymous
  • anonymous
I don't know. Question doesn't specify.
inkyvoyd
  • inkyvoyd
have you only been working with right triangles as of late?
anonymous
  • anonymous
Yes.
inkyvoyd
  • inkyvoyd
if there is an included picture, please draw it. If there isn't one, this is the most ambiguous problem ever.
anonymous
  • anonymous
There isn't. But since they're asking us tp find tank, cos and sin I guess we'll have to assume it's a right triangle?
anonymous
  • anonymous
Think you could just explain the identity you suggested earlier?
inkyvoyd
  • inkyvoyd
Yeah. I was assuming this was a general review question so I pulled a lot of formulas and identities out of my head. Throw those out for now - focuing on the ratios is what is important. "Find sin, cos and tan of a triangle with area :0,465 m^2 side 1: 0,74 cm side 2: 0,0936 cm"
inkyvoyd
  • inkyvoyd
assuming that it is a right triangle, you'll have to do some trial and error. Remember that a^2+b^2=c^2, so try around with values. IN addition, if a and b are legs of the right triangle, you should get ab=2*area (you've been given the area). if you find out which side is which, you can easily progress.
anonymous
  • anonymous
Assuming it isn't, could you explIn tp me the identity you suggested earlier?
inkyvoyd
  • inkyvoyd
does the illustration in the second link (and provided explanation) make sense? http://www.mathopenref.com/triangleareasas.html make sure you go down to "how it works"
anonymous
  • anonymous
Or link to something that does
anonymous
  • anonymous
Yes. Males perfect sense.
anonymous
  • anonymous
Makes*
inkyvoyd
  • inkyvoyd
Okay. So when I saw your problem I instantly figured that was what they were asking about. You can see this even specifies which angle - the included angle. There are two more trig identities that you apply to find the cos and tan of the included angle. I'll link you to the first one.
inkyvoyd
  • inkyvoyd
http://www.regentsprep.org/Regents/math/algtrig/ATT9/pythagoreanid.htm read the first paragraph and tell me if the first identity makes sense. ignore the others.
inkyvoyd
  • inkyvoyd
Since you know the value of sin x you can just bring it into that identity which holds true for all real numbers x, and you can find cos x. THe next step is to find tan x, which is really sin x/cos x here's a simple proof: \(\sin x=\frac{O}{H}\) \(\cos x=\frac{A}{H}\) \(\tan x=\frac{O}{A}\) \(\sin x/\cos x=\frac{O}{H}\frac{H}{A}=\frac{O}{A}=\tan x\) thus for all real x sin x/cos x=tan x
inkyvoyd
  • inkyvoyd
in fact, since you mgiht be curious, I will bring the last thing up - if one wishes to find the sin cos and tangents of the other angles, you will need to use the law of sines and cosines (there is a law of tangents but it's not really used much and I don't know it) THIS STUFF IS EXTRA. Also, you can view the proofs, which are fairly advanced (you will most likely cover this at the end of "regular" trigonometric functions. http://www.regentsprep.org/Regents/math/algtrig/ATT12/derivelawofsines.htm I have to go to bed. Good luck, and happy mathing!
inkyvoyd
  • inkyvoyd
And, if anyone thinks you are too nerdy or it's too early to learn, that's complete bullcrap. I'm a 10th grader as well, and I'm happily enjoying my maths course. Don't let anyone keep you from your potential :P

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