This is an outline that i have to use to find the solution of the question. It involves logarithms and half-angle formulas.I have worked though it but got stuck on some parts. I'd like if you look over my work.
solve the triangle for which given parts are
a=27 ,b=21 ,c=24
Now i used the cosine law and got the answers
A=73 deg 23' 55"
B=48 deg 11' 23"
C=58 deg 24' 43"
...................
okay now for this outline;
a=27
b=21
c=25
----
2s=73
s=36.5
s-a=9.5
s-b=15.5
s-c=11.5
log(s-a)= .97772
log(s-b)=1.19033
log(s-c)=1.06070
--------
=3.22875
log s =1.56229
--------
2)1.66646
--------
log r =0.83323
now this part I'm having trouble with.
log r = 0.83323
log(s-a) = 0.97772
--------
log tan A/2 = 9.85551 - 10
A = ? << can you help me convert.
log r = 0.83323
log (s-b) = 1.19033
--------
log tan B/2 = 9.64290 - 10
B = ? same here my brain freezes
log r = 0.83323
log (s-c) = 1.06070
--------
log tan C/2 = 9.77253 - 10
C = ?
A+B+C= 180 deg 0' 2"
do they match?
--
that was a typo its 15.5 which makes the log entry correct.
=3.22875
log s =1.56229 subtract.
--------
2)1.66646 <<.. then divide by 2 =
--------
log r =0.83323
the reason why i posted the out line was because they did not match. and i didn't understand how you got the inverse tangent .
As I noted in my previous reply to the same question, I fail to understand why you are doing such elaborate steps to solve such a rather simple question.
I always understood, that "solving" a triangle involved finding any missing sides or angles.
The 3 sides were given, you used the cosine law to find the 3 angles.
So to me the triangle is "solved" at that point.
(BTW, I would have found the largest angle by using the Cosine Law, then used the Sine Law to find a second angle, then used the supplementary property to find the third angle. The largest angle would be opposite the largest side. By finding the largest angle using the Cosine Law, you avoid any ambiguous case that might result in using the Sine Law. There can only be one obtuse angle in any triangle. )
for the area, by Heron's Formula,
Area = √(s(s-a)(s-b)(s-c))
= √((36.5)(9.5)(15.5)(11.5))
= 248.6125