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 2 years ago
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!
 2 years ago
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!

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inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.01/2 sin(included angle)* (AB)=area of triangle

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.01/2 sin(angle between 1 and 2)*0,74*0,0936=0,465 solve for sin(angle between 1 and 2)

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0btw, 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
 2 years ago
Best ResponseYou've already chosen the best response.0the 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(1sin x) (pythagorean identity), and to find tan x simply use sin x/cos x

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm,.. Think you could walk me through each step and explain more thoroughly? :/ Not sure I understand your reasoning.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I am using the following formula as an identity: http://www.analyzemath.com/Geometry_calculators/area_triangle_sine.html

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0look at the bottom of this site for a proof http://www.mathopenref.com/triangleareasas.html

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Ah, I think I understand! I'll get back to you if any additional questions arise. You rock.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0good 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)

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.01.) 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
 2 years ago
Best ResponseYou've already chosen the best response.0Well, 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
 2 years ago
Best ResponseYou've already chosen the best response.0And yes, I did not catch that  you would need to convert units (which I didnot do correctly)

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0But what the cos and tan? How do I go about finding them?

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Tried everything, can't figure it out. :/

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0sin^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.

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Think you could explain more in depth? :/

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0have you heard of the identity sin^2 x+cos ^2 x=1?

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0No, never, I'm afraid.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I might be being a bit too advanced then o.o

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, bring it down to my level. :)

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0are 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

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0I'm kust starting to with trigonometric ratios and the like. Just need to know how to attain tan and cos from here.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Okay. Is this a right triangle?

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Just started with trigonometric ratios*

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0I don't know. Question doesn't specify.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0have you only been working with right triangles as of late?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0if there is an included picture, please draw it. If there isn't one, this is the most ambiguous problem ever.

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0There 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?

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Think you could just explain the identity you suggested earlier?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah. 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
 2 years ago
Best ResponseYou've already chosen the best response.0assuming 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.

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Assuming it isn't, could you explIn tp me the identity you suggested earlier?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0does 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"

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Or link to something that does

Veritas45
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. Males perfect sense.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Okay. 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
 2 years ago
Best ResponseYou've already chosen the best response.0http://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
 2 years ago
Best ResponseYou've already chosen the best response.0Since 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
 2 years ago
Best ResponseYou've already chosen the best response.0in 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
 2 years ago
Best ResponseYou've already chosen the best response.0And, 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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