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August 30, 2016
Posted by **Anon** on Saturday, February 26, 2011 at 3:37am.

my question was:

Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30".

give check

You helped me find angle A and B by using logarithms.

A=80 deg 26' 36"

B=67 deg 04' 55"

C=32 deg 28' 30"

a= 21.46

b= 46.28

and I used law of sine to find c.

this is my answer and i would appreciate if you correct me if I'm wrong.

sinA/a = sinC/c

sin 80.443 /21.46 = sin 32.475/c

21.46 (sin 32.475)/(sin 80.443)c

c= 11.68

okay now it says to give check.

okay i honestly don't know how or if the law of sin already covers the check part. I'd like your advice.

and thank you again . I honestly love it when i understand something i thought was so confusingly impossible to understand before.

- trigonometry (repost) Mathmate -
**drwls**, Saturday, February 26, 2011 at 6:54amYou can check your value of c by using the Law of Cosines, with the original calyues of a, b and C.

c^2 = a^2 + b^2 -2ab cos C

c^2 = 460.32 +2141.84 -1986.34*0.8436

c = 30.44

That is not what you came up with. There appears to be something wrong with your initial angles. The law of sines does not agree with your angles A and B. If A > B, than you should have a > b

Perhaps Mathmate can explain the origin of the problem. - trigonometry (repost) Mathmate -
**MathMate**, Saturday, February 26, 2011 at 9:31amI have looked at the question, and confirm that there was an error in the previous calculations using the law of tangents. Following are results using the sine rule:

Given:

a = 21.46, b = 46.28, C = 32-28-30

The cosine rule gives:

c = sqrt(a^2+b^2-2*a*b*cos(C))=30.440833

The sine rule gives

A=22-14-32, and

B=125-16-58

If you draw the triangle, with C=32°, a=21.46 and b=46.28, you will see a skew triangle which shows obviously that B>90°.

So sin(A) has to be interpreted as 180 - arcsin() of the acute angle, which gives 125-16-58 (instead of 54-43-02 straight from the calculator).

I have not completed looking into the source of the error of my previous calculations. It may have to do with the interpretation of the atan() values. I will get back to you when it is done.

I apologize for the inconvenience. - trigonometry (repost) Mathmate -
**MathMate**, Saturday, February 26, 2011 at 10:05amI just took another look. The formula for the law of tangents should have been tan((A+B)/s)/tan((A-B)/2)=(a+b)/(a-b).

Previously I have not divided the angles by 2, hence the error.

I will try to make a corrected version and repost in the original post. - trigonometry (repost) Correction -
**MathMate**, Saturday, February 26, 2011 at 6:16pmThe correction to the problem using the tangent rule has been posted at the original post:

http://www.jiskha.com/display.cgi?id=1298609593

Sorry for the inconvenience so caused.