hi to all:

2. ## Re: Find the ANGLE

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.

3. ## Re: Find the ANGLE

Originally Posted by waqarhaider
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.

4. ## 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

5. ## Re: Find the ANGLE

Hello again eazemsoft,
My calcs do not need any info about angle ACD. In this case it is acute.

6. ## 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

7. ## Re: Find the ANGLE

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).

8. ## 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

9. ## Re: Find the ANGLE

my solution in attachment --> good problem

10. ## 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.

11. ## Re: Find the ANGLE

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???

12. ## Re: Find the ANGLE

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.

13. ## Re: Find the ANGLE

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,

and this answer changes both angles.

14. ## Re: Find the ANGLE

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

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

15. ## Re: Find the ANGLE

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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