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Math Help - Find the ANGLE

  1. #1
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    Find the ANGLE

    hi to all:
    can you please help me to find the angle BAC:

    Find the ANGLE-q1.jpg
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  2. #2
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    Re: Find the ANGLE

    Follow the steps below:
    1. from triangle ABD find AB & AD using cosine rule.
    2. find AC from given equation
    3.find CD from right triangle ACD
    4.find BC from triangle BCD
    Now you has all three sides of triangle ABC, and can find m<BAC.
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  3. #3
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    Re: Find the ANGLE

    Quote Originally Posted by waqarhaider View Post
    Follow the steps below:
    1. from triangle ABD find AB & AD using cosine rule.
    2. find AC from given equation
    3.find CD from right triangle ACD
    4.find BC from triangle BCD
    Now you has all three sides of triangle ABC, and can find m<BAC.
    ACD is NOT a right triangle

    angle ACD > 90 deg.
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  4. #4
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    Re: Find the ANGLE

    Hello razemsoft,
    My answer is 45.2 degrees obtained using the sign law for AD. AC from given equation.DC from cosine law(angle 50). Angle DAC from cosine law. BAC = 100 - DAC
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  5. #5
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    Re: Find the ANGLE

    Hello again eazemsoft,
    My calcs do not need any info about angle ACD. In this case it is acute.
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  6. #6
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    Re: Find the ANGLE

    Dear Razemsoft,
    I noted an error in my calcs and when I corrected this I found that DC can have two solutions. The shorter one gives the obtuse ACD angle.I did not go further
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  7. #7
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    Re: Find the ANGLE

    Quote Originally Posted by bjhopper View Post
    Hello again razemsoft21,
    My calcs do not need any info about angle ACD. In this case it is acute.
    Hello bjhopper,
    I got the answer of (40 deg. for BAC)
    and (70 deg. for ACD)
    but this answer doesn't satisfy the condition (ACD > 90 degs).
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  8. #8
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    Re: Find the ANGLE

    Hi razemsoft,
    I followed thru from post5 to get a corrected solution.Here are my answers. I increased the figure 10 times to avoid fractions less than 1

    AD = 9.54 AC= 7.78 DC= 3.48 Angle DAC = 20 degrees Angle BAC =80 degrees Angle ACD = 110 degrees
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  9. #9
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    Re: Find the ANGLE

    my solution in attachment --> good problem
    Attached Thumbnails Attached Thumbnails Find the ANGLE-8-13-2011-5-37-50-pm.png  
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  10. #10
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    Re: Find the ANGLE

    hi mido22,
    Thank you for helping.

    by drawing the shape using math program on my PC

    it shows that the angle CAD > 1

    and angle BAC < 99

    something wrong.
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  11. #11
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    Re: Find the ANGLE

    Quote Originally Posted by razemsoft21 View Post
    hi mido22,
    Thank you for helping.

    by drawing the shape using math program on my PC

    it shows that the angle CAD > 1

    and angle BAC < 99

    something wrong.
    that is with proof nothing wrong but angle CAD was 1.2 and some decimals so it won't affect so much also same for angle BAC
    if u have other opinion can u write the correct proof???
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  12. #12
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    Re: Find the ANGLE

    Quote Originally Posted by bjhopper View Post
    Hi razemsoft,
    I followed thru from post5 to get a corrected solution.Here are my answers. I increased the figure 10 times to avoid fractions less than 1

    AD = 9.54 AC= 7.78 DC= 3.48 Angle DAC = 20 degrees Angle BAC =80 degrees Angle ACD = 110 degrees

    hi bjhopper,
    thanks for sharing.
    can you please give me some explaination for these answers.
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  13. #13
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    Re: Find the ANGLE

    Quote Originally Posted by mido22 View Post
    that is with proof nothing wrong but angle CAD was 1.2 and some decimals so it won't affect so much also same for angle BAC
    if u have other opinion can u write the correct proof???
    I mean the accuracy of your calculations,

    AD = sin (70) / sin (100) = 0.954 ---> your answer = 0.946

    and this answer changes both angles.
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  14. #14
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    Re: Find the ANGLE

    Quote Originally Posted by razemsoft21 View Post
    I mean the accuracy of your calculations,

    AD = sin (70) / sin (100) = 0.954 ---> your answer = 0.946

    and this answer changes both angles.
    hmmm ok u can use steps and get the accurate answers ... i didn't know that 0.01 will affect with u so much so i'm so sry but what i can do is to give u my proof to follow it
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  15. #15
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    Re: Find the ANGLE

    Quote Originally Posted by mido22 View Post
    hmmm ok u can use steps and get the accurate answers ... i didn't know that 0.01 will affect with u so much so i'm so sry but what i can do is to give u my proof to follow it
    Thanks a lot for the steps (logically true)

    but this 0.01 changes 1 degree to 20 degrees
    and changes angle BAC from 99 degrees to 80 degrees.

    again thank you for the logical method.
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