Trigonometric ratios in right triangles (article) | Khan Academy (2024)

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• Bhavlabhya

  7 years agoPosted 7 years ago. Direct link to Bhavlabhya's post “hey I have a questionwha...”

  hey I have a question
  what if we have a triangle with no known sides but 2 angles(including one right angle) is given then how will we find the 3rd angle and 3 sides? is it possible?

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  (32 votes)

  • 490139

    2 years agoPosted 2 years ago. Direct link to 490139's post “If you know two angles of...”

    

    

    

    If you know two angles of a triangle, it is easy to find the third one. Since the three interior angles of a triangle add up to 180 degrees you can always calculate the third angle like this:

    Let's suppose that you know a triangle has angles 90 and 50 and you want to know the third angle. Let's call the unknown angle x.
    x + 90 + 50 = 180
    x + 140 = 180
    x = 180 - 140
    x = 40

    As for the side lengths of the triangle, you need more information to figure those out. A triangle of side lengths 10, 14, and 9 has the same angles as a triangle with side lengths of 20, 28, and 18.

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    (64 votes)
• Ira Kulkarni

  7 years agoPosted 7 years ago. Direct link to Ira Kulkarni's post “How is theta defined in a...”

  How is theta defined in accurate mathematical language?

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  (16 votes)

  • David Severin

    7 years agoPosted 7 years ago. Direct link to David Severin's post “theta is not defined in m...”

    

    

    theta is not defined in math language, it is a symbol used as a variable to generally represent an angle.

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    (27 votes)
• V

  6 years agoPosted 6 years ago. Direct link to V's post “What is the etymology of ...”

  See Also

  Right TrianglesAre Trigonometric functions only for right triangles? | SocraticWhy is Trigonometry hard? (7 reasons with solutions to master this subject) - Maths How To with AnitaNumeracy, Maths and Statistics - Academic Skills Kit

  What is the etymology of sin, cos and tan?

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  (15 votes)

  • ianXmiller

    6 years agoPosted 6 years ago. Direct link to ianXmiller's post “*From Wikipedia - Trigono...”

    

    

    

    From Wikipedia - Trigonometric Functions - Etymology

    The word sine derives from Latin sinus, meaning "bend; bay", and more specifically "the hanging fold of the upper part of a toga", "the bosom of a garment", which was chosen as the translation of what was interpreted as the Arabic word jaib, meaning "pocket" or "fold" in the twelfth-century translations of works by Al-Battani and al-Khwārizmī into Medieval Latin. The choice was based on a misreading of the Arabic written form j-y-b (جيب), which itself originated as a transliteration from Sanskrit jīvā, which along with its synonym jyā (the standard Sanskrit term for the sine) translates to "bowstring", being in turn adopted from Ancient Greek χορδή "string".

    The word tangent comes from Latin tangens meaning "touching", since the line touches the circle of unit radius, whereas secant stems from Latin secans—"cutting"—since the line cuts the circle.

    The prefix "co-" (in "cosine", "cotangent", "cosecant") is found in Edmund Gunter's Canon triangulorum (1620), which defines the cosinus as an abbreviation for the sinus complementi (sine of the complementary angle) and proceeds to define the cotangens similarly.

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    (55 votes)
• akshaysheriff

  7 years agoPosted 7 years ago. Direct link to akshaysheriff's post “IS there ANY way to easil...”

  IS there ANY way to easily remember the SIN, COS and TAN formulas?? Any tips and tricks?

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  (2 votes)

  • John

    3 years agoPosted 3 years ago. Direct link to John's post “SOH CAH TOA. The sine of ...”

    

    SOH CAH TOA. The sine of theta, θ, or sine(θ = opposite side divided by hypotenuse, cosine(θ = adjacent side divided by hypotenuse, and tangent(θ = opposite divided by adjacent side. Or SOH CAH TOA

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    (16 votes)
• Brendon Josh Orate

  6 years agoPosted 6 years ago. Direct link to Brendon Josh Orate's post “Based on the first paragr...”

  Based on the first paragraph, "The ratios of the sides of a right triangle are called trigonometric ratios.", if in trigonometry the ratios of the sides of a triangle are called 'trigonometric ratios' then what if the triangle is not a right triangle. Will the ratios of the sides of that triangle have a different label. And based on my question, how will the mnemonic 'soh cah toa' help find the sides of the 'non- right triangle' triangle? Are there more methods to find the sides of a triangle relative to trigonometric functions or formula?

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  (5 votes)

  • Scott Freeman

    6 years agoPosted 6 years ago. Direct link to Scott Freeman's post “Good questions, it's clea...”

    See Also

    Geometry Unit 8 in High School: Mathematics - Montgomery County Public Schools, Rockville, MD | Montgomery County Public Schools

    

    Good questions, it's clear you are thinking about where this is going. The laws of sines and cosines can be used to help you figure out the relationships of the sides and angles for triangles that are not right triangles. There are some great videos:

    https://www.khanacademy.org/math/geometry/hs-geo-trig/modal/v/law-of-sines

    https://www.khanacademy.org/math/geometry/hs-geo-trig/modal/v/law-of-cosines-example

    https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solving-general-triangles/v/law-of-cosines-word-problem

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    (18 votes)
• Rishika

  8 years agoPosted 8 years ago. Direct link to Rishika's post “How to find the sin, cos ...”

  How to find the sin, cos and tan of the 90 degree angle? Will we follow the same procedure as we did with the other two angles?

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  (7 votes)

  • kubleeka

    8 years agoPosted 8 years ago. Direct link to kubleeka's post “If we consider the right ...”

    

    If we consider the right angle, the side opposite is also the hypotenuse. So sin(90)=h/h=1.
    By pythagorean theorem, we get that sin^2(90)+cos^2(90)=1. So, substituting, 1+cos^2(90)=1
    cos^2(90)=0
    cos(90)=0

    And we see that tan(90)=sin(90)/cos(90)=1/0. So tan(90) is undefined.

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    (12 votes)
• kubleeka

  8 years agoPosted 8 years ago. Direct link to kubleeka's post “I've heard that there are...”

  I've heard that there are other trigonometric functions out there, with names like versine. Who decided that sine, cosine, and tangent would be the ones we learn in school? What happened to the others?

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  (6 votes)

  • David Calkins

    8 years agoPosted 8 years ago. Direct link to David Calkins's post “I would guess that it's b...”

    

    I would guess that it's because these functions are technically more complex than the ones we learn in school. For example, versine(x) = 1 - cos(x). Applications of these functions seem to be applicable to navigation, especially across a spherical plane. However, with the progression of technology (I assume) these older functions have grown less practical and have fallen away in favor of manipulations of the more familiar 6 trig functions we study today.

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    (11 votes)
• jee002

  a year agoPosted a year ago. Direct link to jee002's post “What is the symbol theta”

  What is the symbol theta

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  (4 votes)

  • Raz

    a year agoPosted a year ago. Direct link to Raz's post “Theta is a Greek letter t...”

    

    Theta is a Greek letter that is commonly used in Math to symbolize a variable that represents an angle :)

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    (11 votes)
• 201100879

  a year agoPosted a year ago. Direct link to 201100879's post “Can you explain the multi...”

  Can you explain the multiple choice question, The Khan explanation didn't really help me.

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  (2 votes)

  • Aeternum

    a year agoPosted a year ago. Direct link to Aeternum's post “First, let's think about ...”

    

    First, let's think about the rules of SOH-CAH-TOA:
    SOH -> Sine = Opposite / Hypotenuse
    CAH -> Cosine = Adjacent / Hypotenuse
    TOA -> Tangent = Opposite / Adjacent
    This is relative to the value of the angle inputted into each of these functions.

    The question is asking us which of the follow values is equal to a/c. Note that you can select multiple answers, which provides a hint as to how many answers you should get. Let's evaluate them, one by one:

    cos(20) -> CAH -> cos(20) = Adjacent / Hypotenuse -> b / c
    sin(20) -> SOH -> sin(20) = Opposite / Hypotenuse -> a / c
    tan(20) -> TOA -> tan(20) = Opposite / Adjacent -> a / b
    cos(70) -> CAH -> cos(70) = Adjacent / Hypotenuse -> a / c
    sin(70) -> SOH -> sin(70) = Opposite / Hypotenuse -> b / c
    tan(70) -> TOA -> tan(70) = Opposite / Adjacent -> b / a

    Out of these 6 answer choices, only sin(20) and cos(70) produce the desired result of a / c. Hence, they are the two answers.

    I hope this clarified the question for you. If not, feel free to comment and ask away!

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    (15 votes)
• ivanov

  5 years agoPosted 5 years ago. Direct link to ivanov's post “why is sin, cos and tan c...”

  why is sin, cos and tan change?

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  (3 votes)

  • _______

    5 years agoPosted 5 years ago. Direct link to _______'s post “sin cos and tan changes b...”

    

    sin cos and tan changes based on the angle you choose.it is all matter of perspective.

    Comment on _______'s post “sin cos and tan changes b...”

    (11 votes)