Laws of sines and cosines review (article) | Khan Academy (2024)

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• victoria

  4 years agoPosted 4 years ago. Direct link to victoria's post “I want to know why this a...”

  I want to know why this article says "Remember that if the missing angle is obtuse, we need to take 180 degrees and subtract what we got from the calculator" when using the law of sines to find a missing angle. Are there videos that explain why this is? I don't understand why during calculations it won't just give the obtuse angle, and instead gives an acute angle.

  I'm only taking this geometry course and there is nothing along the way that explains this, not even the videos that introduce the law of sines.

  Thanks.

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  (33 votes)

  • cossine

    4 years agoPosted 4 years ago. Direct link to cossine's post “There can be two since si...”

    

    

    There can be two since sin(theta) = sin(180-theta) for all values of theta that are real numbers e.g. -1000.98, sqrt(2) etc.

    Since you are using the sin^-1 function you will only ever get 1 angle as the range is defined from -90 to 90 degrees(which is -pi/2 to pi/2 in radians). You can it sketch on desmos to see what it look likes.

    So if you need to find an obtuse angle then you need to use 180-theta to find the obtuse angle.

    It might be helpful to take look at videos related function as well.

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    (32 votes)
• Micron

  8 years agoPosted 8 years ago. Direct link to Micron's post “in problem 3.3 I had to o...”

  in problem 3.3 I had to open the explanation and do not understand why the law of sines in this solution is switched to sin(c)/length of side. isnt it usually the other way around??

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  (11 votes)

  • Shrey Joshi

    8 years agoPosted 8 years ago. Direct link to Shrey Joshi's post “Hello Candacemhazelwood,...”

    Hello Candacemhazelwood,

    The law of sines states:

    sin(a)/A = sin(b)/B = sin(c)/C

    when angle a is opposite side a
    when angle b is opposite side B
    and
    when angle c is opposite side c

    Hope this helps:
    https://www.khanacademy.org/math/geometry-home/right-triangles-topic/law-of-sines-geo/v/law-of-sines solve for side

    https://www.khanacademy.org/math/geometry-home/right-triangles-topic/law-of-sines-geo/v/law-of-sines-example - solve for angle

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    (7 votes)

    See Also

    22 Epic Activities to Reinforce the Law of Sines and Cosines - Teaching Expertise3.4: Chapter 3 Activity
• Teagana

  8 years agoPosted 8 years ago. Direct link to Teagana's post “I can't find anything her...”

  I can't find anything here about ambiguous triangles. What if a question asks you to solve from a description where two triangles exist? Like "Determine the unknown side and angles in each triangle, if two solutions are possible, give both: In triangle ABC, <C = 31, a = 5.6, and c = 3.9." I solved for height and see that two solutions exist, and the answer key in my textbook agrees, but I can't figure out how to get either. From a set of questions that's only supposed to be on sine law.

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  (5 votes)

  • Jordan Cooper

    8 years agoPosted 8 years ago. Direct link to Jordan Cooper's post “Use the Law of Sines to g...”

    

    Use the Law of Sines to get one possible angle A:
    sin(A)/a=sin(C)/c
    sin(A)/5.6=sin(31)/3.9
    sin(A)=5.6sin(31)/3.9
    A=arcsin(5.6sin(31)/3.9)=47.6924

    Subtract 31 (C) and this angle (A) from 180 to find the third angle (B=101.3076) and use the Law of Sines again to find the third side. If you use the given angle-side pair (C and c) you will be less likely to incur error from your own rounding of angle A:
    b/sin(B)=c/sin(C)
    b/sin(101.3076)=3.9/sin(31)
    b=3.9sin(101.3076)/sin(31)=7.4253

    But if you know that supplementary angles share a sine value, you know that A can also be an obtuse angle with the same sine as 47.6924:
    A=180-47.6924=132.3076

    And again, subtract 31 (C) and the obtuse angle A from 180 to find the other possible third angle (B=16.6924) and use the Law of Sines to find the other possible third side, again using angle C and side c to avoid errors from rounding:
    b/sin(B)=c/sin(C)
    b/sin(16.6924)=3.9/sin(31)
    b=3.9sin(16.6924)/sin(31)=2.1750

    It all comes from knowing that there are two angles, one obtuse and one acute, for every sine value. And you find the obtuse one by subtracting the acute one from 180.

    If you try to do this with a unique triangle (one without two possible sets of angles and sides) your given angle and the obtuse angle you find will add up to more than 180, and so if you try to find a third angle to go with the obtuse one, your subtraction will tell you the third angle is negative, at which point you know you're going down a nonsensical mathematical road, and there weren't two possible triangles to begin with.

    Good luck!

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    (17 votes)
• AgamBhai

  a year agoPosted a year ago. Direct link to AgamBhai's post “What is the law of tangen...”

  What is the law of tangents used for??

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  (1 vote)

  • ryan1014

    a year agoPosted a year ago. Direct link to ryan1014's post “The law of tangents is us...”

    

    The law of tangents is used to keep people from getting to the point. Old people tend to use it a lot :)

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    (18 votes)
• Jonathan

  5 years agoPosted 5 years ago. Direct link to Jonathan's post “So, obviously, there is t...”

  So, obviously, there is the law of sines and the law of cosines. That is what this entire section has been about. However, I'm curious about if there is such a thing as the law of tangents. Since there is both sine and cosine, wouldn't it make sense if there was something like the law of tangents?

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  (8 votes)

  • Cochran

    5 years agoPosted 5 years ago. Direct link to Cochran's post “Yes there is. Though I wi...”

    Yes there is. Though I will admit that the only way I know that is by looking it up. I assumed that was but wasn't certain. You can probably find the exact statement of the law on Wikipedia or some math site.

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    (3 votes)
• Bartholomew

  8 months agoPosted 8 months ago. Direct link to Bartholomew's post “I'm not sure if anyone no...”

  I'm not sure if anyone noticed this, but in the exercise they put this guy Dennis as having to jump 17.4 feet across a rooftop. I looked it up, I don't think he survived.

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  (7 votes)
• Utkarsh Sharma

  4 years agoPosted 4 years ago. Direct link to Utkarsh Sharma's post “In the Video 'Solving An ...”

  In the Video 'Solving An Angle With The Law Of Sines' at

  2:05

  , Sal said that Law of Sines is 'sin(a)/A = sin(b)/B = sin(c)/C (lower case letters are the angles and the upper case letters are the side opposite to the angle), in this article it says 'A/sin(a) = B/sin(b) = C/sin(c)'. So which one should I choose?

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  (4 votes)

  • Jeff Dodds

    4 years agoPosted 4 years ago. Direct link to Jeff Dodds's post “The Law of Sines can be w...”

    The Law of Sines can be written either way! You can put the angles in the numerators and the sides in the denominators, or the other way around.

    To understand why, think about this true equation:

    1/2 = 2/4 = 3/6

    It's still true if we reverse the numerators and denominators:

    2/1 = 4/2 = 6/3

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    (5 votes)
• Joshua

  7 years agoPosted 7 years ago. Direct link to Joshua's post “If law of sines is a/sin(...”

  If law of sines is a/sin(a)=b/sin(b)=c/sin(c), does sin(a)/a=sin(b)/b=sin(c)/c work?

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  (3 votes)

  • kubleeka

    7 years agoPosted 7 years ago. Direct link to kubleeka's post “Yes. Just raise one of th...”

    Yes. Just raise one of those equations to the -1 power, and you get the other equation. They're equivalent.

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    (6 votes)
• Pierre Dob

  a year agoPosted a year ago. Direct link to Pierre Dob's post “Is this a correct way to ...”

  Is this a correct way to check whether you use the law of sines or law of cosines? If you have two angles and a side or two sides and an angle, use the law of sines, if you have 3 sides use the law of cosines. Is there anything you need to add to this list?

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  (4 votes)

  • kubleeka

    a year agoPosted a year ago. Direct link to kubleeka's post “The law of sines works on...”

    The law of sines works only if you know an angle, a side opposite it, and some other piece of information. If you know two sides and the angle between them, the law of sines won't help you.

    In any other case, you need the law of cosines.

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    (3 votes)
• nandhu27

  4 years agoPosted 4 years ago. Direct link to nandhu27's post “What is the numeric form ...”

  What is the numeric form of sine, cosine, and tangent? Like what does the calculator use to calculate trig functions?

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  (3 votes)

  • kubleeka

    4 years agoPosted 4 years ago. Direct link to kubleeka's post “The trig functions can be...”

    The trig functions can be expressed as polynomials of infinite degree, called Taylor polynomials. For example, sin(x)=x-x³/6 +x⁵/120 -x⁷/5040+... Some calculators use these series to approximate the values of the trig functions, as well as other functions like exponentials.

    You'll develop Taylor polynomials in calculus.

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    (4 votes)