Find the ANGLE

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• Aug 11th 2011, 07:49 AM
razemsoft21
Find the ANGLE
hi to all:
can you please help me to find the angle BAC:

Attachment 22026
• Aug 11th 2011, 11:52 AM
waqarhaider
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.
• Aug 12th 2011, 04:15 AM
razemsoft21
Re: Find the ANGLE
Quote:

Originally Posted by waqarhaider
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.
• Aug 12th 2011, 08:58 AM
bjhopper
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
• Aug 12th 2011, 09:27 AM
bjhopper
Re: Find the ANGLE
Hello again eazemsoft,
My calcs do not need any info about angle ACD. In this case it is acute.
• Aug 12th 2011, 12:23 PM
bjhopper
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
• Aug 13th 2011, 01:58 AM
razemsoft21
Re: Find the ANGLE
Quote:

Originally Posted by bjhopper
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).
• Aug 13th 2011, 05:46 AM
bjhopper
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
• Aug 13th 2011, 08:36 AM
mido22
Re: Find the ANGLE
my solution in attachment --> good problem (Cool)
• Aug 13th 2011, 05:15 PM
razemsoft21
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.
• Aug 13th 2011, 05:18 PM
mido22
Re: Find the ANGLE
Quote:

Originally Posted by razemsoft21
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???
• Aug 13th 2011, 05:22 PM
razemsoft21
Re: Find the ANGLE
Quote:

Originally Posted by bjhopper
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.
• Aug 13th 2011, 05:34 PM
razemsoft21
Re: Find the ANGLE
Quote:

Originally Posted by mido22
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.
• Aug 13th 2011, 05:37 PM
mido22
Re: Find the ANGLE
Quote:

Originally Posted by razemsoft21
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
• Aug 13th 2011, 05:50 PM
razemsoft21
Re: Find the ANGLE
Quote:

Originally Posted by mido22
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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