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Math Help - cosine rule

  1. #1
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    cosine rule

    could any one help please..yet to be taught the cosine rule but trying to learn it myself but un sure what buttons to press on my calculator..
    i have a triangle A, B,F. <A=52 side f=3000 and b=6000..i need to find the other side and two angles..
    thanks
    jim
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  2. #2
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    Quote Originally Posted by jim49990 View Post
    could any one help please..yet to be taught the cosine rule but trying to learn it myself but un sure what buttons to press on my calculator..
    i have a triangle A, B,F. <A=52 side f=3000 and b=6000..i need to find the other side and two angles..
    thanks
    jim
    The cosine rule for your triangle is:

    a^2=f^2+b^2-2fc cos(A),

    since everything on the right hand side is a known you can find
    a fairly easily.

    Now the sine rule will allow you to find the remaining angles:

    a/sin(A)=b/sin(B)=f/sin(F).

    RonL
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  3. #3
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    answer

    so would that give me a answer of 10190.00
    thanks
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  4. #4
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    Quote Originally Posted by jim49990 View Post
    so would that give me a answer of 10190.00
    thanks
    a^2=3000^2+6000^2-2*3000*6000 cos(52),

    a^2=(9+36-36x0.61566)*1000^2=30.2232 1000^2

    so:

    a=sqrt(22.836)*1000~=4778.72

    RonL
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  5. #5
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    still stuck

    sorry to be a pain but i am still struggling on what buttons to press on my calculator
    jim
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  6. #6
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    Quote Originally Posted by jim49990 View Post
    sorry to be a pain but i am still struggling on what buttons to press on my calculator
    jim
    Don't try to do it in one go on your calculator, they all differ and may not
    behave in the same way as someone elses calculator.

    Find 3000^3, and 6000^2, 3000*6000 and cos(52), these are single stage
    operations then write out what what you now have to calculate.

    So cos(52)=0.615661 (clear the calculator, make sure you are in degrees
    mode, then enter 52 and hit the cos button to get this, write it down).

    3000^2=9e6 (which means 9 * 1000000, clear the calculator enter 3000
    then hit the x^2 key, or enter x 3000 =)
    6000^2=3.6e7 (which means 36 *1000000, as above)

    3000*6000=1.8e7 (which means 18 * 1000000)

    then calculate:

    9e6+3.6e7-2*3.6e7*0.61661=22836.204

    then hit the square root key to get 4778.7..

    RonL
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  7. #7
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    Talking many thanks

    cheers mate..i owe you a drink
    jim
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  8. #8
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    angles

    would <f =29 degrees
    thanks
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  9. #9
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    Quote Originally Posted by jim49990 View Post
    would <f =29 degrees
    thanks
    I make it 29.62 degrees.

    Unsing the sine rule you should have:

    sin(F)/f=sin(A)/a,

    so

    sin(F)=f*sin(A)/a=3000*sin(52)/4778.2=0.627851*0.78801=0.494752

    and asin(0.494752)~=29.62 degrees

    RonL
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  10. #10
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    Hello, Jim!

    Could any one help please?
    Yet to be taught the cosine rule but trying to learn it myself
    but unsure what buttons to press on my calculator.

    I have a triangle ABF with: A = 52^o,\;f = 3000,\;b = 6000
    I need to find the other side and two angles.

    To find side a\!:\; a^2\;=\;b^2 + f^2 - 2bf\cos A

    We have: . a^2\;=\;6000^2 + 3000^2 - 2\!\cdot\!6000\!\cdot\!3000\cos52^o

    Be sure your calculator is in degree mode.

    On your calculator, enter:

    . . 6000\;\;\boxed{x^2}\;\;\boxed{+}\;\;3000\;\;\boxed  {x^2}\;\;\boxed{-}\;\;2\;\;\boxed{\times}\;\;6000\;\;\boxed{\times}  \;\;3000\;\;\boxed{\times}\;\;\boxed{\cos}\;\;52\;  \;\boxed{=}

    It is essential that you press \boxed{=} at the end of this line.

    . . Then press: . \boxed{\land}\;\;0.5\;\;\boxed{=}<br />

    You should get: . a\;=\;4778.722307\quad\Rightarrow\quad\boxed{a\;\a  pprox\;4778.7}


    To find angle B:\;\frac{\sin B}{b} \,=\,\frac{\sin A}{a}\quad\Rightarrow\quad \sin B \,=\,\frac{b\sin A}{a}

    We have: . \sin B\:=\:\frac{6000\sin52^o}{4778.7}

    Enter: . 6000\;\;\boxed{\times}\;\;\boxed{\sin}\;\;52\;\;\b  oxed{)}\;\;\boxed{\div}\;\;4778.7\;\;\boxed{=} . . . . and get: 0.989403922

    Press \boxed{\sin^{-1}}\;\;\boxed{\text{Ans}}\;\;\boxed{=} . . . . and get: 81.65176939

    Hence: . B \:\approx\:81.65^o\quad\hdots\quad \text{or: }B \:\approx\:98.35^o **

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    If B = 81.65^o, then: . F \:=\:180^o - 52^o - 81.65^o \:=\:46.35^o

    We have: . \boxed{\begin{array}{ccc}A\:= \\ B\:= \\ F\;=\end{array}<br />
\begin{array}{ccc}52^o \\ 81.65^o \\ 46.35^o\end{array}<br />
\begin{array}{ccc}a\:= \\ b\:= \\ f\:=\end{array}<br />
\begin{array}{ccc}4778.7 \\ 6000 \\ 3000\end{array}}


    But this doesn't check out . . .

    . . \frac{a}{\sin A} \:=\:\frac{4778.7}{\sin52^o} \:\approx\:6064.257

    . . \frac{b}{\sin B} \:=\:\frac{6000}{\sin81.35^o} \:\approx\:6064.284

    . . \frac{f}{\sin F} \:=\:\frac{3000}{\sin46.35^o}\:\approx\:4146.110 ??

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    **

    Whenever we use \boxed{\sin^{-1}}, there are always two possible answers.
    One is the acute angle on your calculator screen,
    . . the other is its supplement (subtract from 180)

    The calculator said B = 81.65^o, which didn't work.
    . . So it must be: . B \:=\:180^o - 81.65^o \:=\:98.35^o

    If B = 98.35^o, then F\:=\:180^o - 52^o - 98.35^o \:=\:29.65^o

    The solution is: . \boxed{\begin{array}{ccc}A\:=\\B\:=\\F\:=\end{arra  y}<br />
\begin{array}{ccc}52^o\\98.35^o\\29.65^o\end{array  }<br />
\begin{array}{ccc}a\:=\\b\:=\\f\:=\end{array}<br />
\begin{array}{ccc}4778.7 \\ 6000 \\ 3000\end{array}}

    . . and these check out . . .

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