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tan help needed

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    theta is an acute angle and sin theta =1/4 find the exact value of tan

    isnt tan=costheta/sintheta?

    how do i answer this
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    If sin = 1/4

    then opp=1 and hyp=4

    what is adj

    hence what is tan
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    --- mistake
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    (Original post by TenOfThem)
    If sin = 1/4

    then opp=1 and hyp=4

    what is adj

    hence what is tan
    tan is o/a

    so i know what opposite is as its 1

    but i dont have the adjacent
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    (Original post by TenOfThem)
    If sin = 1/4

    then opp=1 and hyp=4

    what is adj

    hence what is tan
    is the h square root of 5
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    (Original post by dongonaeatu)
    tan is o/a

    so i know what opposite is as its 1

    but i dont have the adjacent
    but you do have 2 sides so surely you know how to find adj
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    (Original post by dongonaeatu)
    is the h square root of 5
    no, h = 4
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    (Original post by TenOfThem)
    but you do have 2 sides so surely you know how to find adj
    is it square root of 5
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    (Original post by TenOfThem)
    no, h = 4
    sorry, is adjacent square root of 5
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    (Original post by dongonaeatu)
    is it square root of 5
    no

    how do you get that
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    (Original post by dongonaeatu)
    theta is an acute angle and sin theta =1/4 find the exact value of tan

    isnt tan=costheta/sintheta?

    how do i answer this
    sin(T) = opp/hyp

    So draw out the triangle. Use Pythagoras (hyp^2 = adj^2 x opp^2) to calculate adj

    tan(T) = opp/adj
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    (Original post by TenOfThem)
    no

    how do you get that
    is it 5^2
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    (Original post by dongonaeatu)
    is it 5^2
    What are you doing to get these numbers

    You have a right angled triangle

    The Hyp = 4

    The Opp = 1

    You are looking for the third side


    Remind me what exam level you are studying for
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    (Original post by lukas1051)
    sin(T) = opp/hyp

    So draw out the triangle. Use Pythagoras (hyp^2 = adj^2 x opp^2) to calculate adj

    tan(T) = opp/adj
    doesnt it equal 5 then?
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    (Original post by TenOfThem)
    What are you doing to get these numbers

    You have a right angled triangle

    The Hyp = 4

    The Opp = 1

    You are looking for the third side


    Remind me what exam level you are studying for
    okay so pythagorus therom a^2+b^2=c^2
    4^2+1^2=c^2
    16+1=c^2
    c= square root of 17
    so the a = square root of 17?
    AS level c2
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    I don't know how much trigonometry you know, but I'll try and be as simple as possible. sin is opposite over hypotenuse, tangent is opposite over adjacent. Since sinx=1/4, we assume the opposite is 1 and the hypotenuse is 4. Pythagoras' theorem tells us that the adjacent length is sqrt(15). Hence, tanx=1/sqrt(15).
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    so from sin(x) = 1/4 we know that:

    opp= 1 hyp= 4

    so by Pythagoras' Theorem: opp^2 + adj^2= hyp^2

    rearranging to get adj = sqrt(hyp^2-opp^2)

    so adj = sqrt(4^2 - 1^2) = sqrt(16 - 1) = sqrt(15)

    And as tan(x) = opp/adj

    so tan(x) = 1/sqrt(15)
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    (Original post by dongonaeatu)
    okay so pythagorus therom a^2+b^2=c^2
    4^2+1^2=c^2
    16+1=c^2
    c= square root of 17
    so the a = square root of 17?
    AS level c2
    Remember c is the longest side! So you have 1+b^2=16.
    b=sqrt(15)
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    (Original post by dongonaeatu)
    okay so pythagorus therom a^2+b^2=c^2
    4^2+1^2=c^2
    16+1=c^2
    c= square root of 17
    so the a = square root of 17?
    AS level c2
    c = hypotenuse..

    so a^2 + b^2 = c^2

    a^2 + 1^2 = 4^2
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    (Original post by dongonaeatu)
    okay so pythagorus therom a^2+b^2=c^2
    4^2+1^2=c^2
    16+1=c^2
    c= square root of 17
    so the a = square root of 17?
    AS level c2
    No. The hypotenuse, c = 4. You are looking for the adjacent side (a or b)

    4^2 = 1^2 + b^2

    4^2 - 1^2 = b^2

    16 - 1 = b^2

    15 = b^2

    b = adj = sqrt(15)

    You now how the opposite and adjacent sides. What does tan(T) now equal?

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