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.

Question

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
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?

Answer 1

I noticed an error in your outline
log(s-b) = log 15 = 1.17609 you have 1.19033

Your outline suggests to me Heron's formula for finding the area of a triangle.
I didn't see anything about area of triangle in your question

then I see log r =0.83323
where does r come from ?

To do a calculation like
log tan A/2 = 9.85551 - 10
A = ?
I had already shown you how to do that in one of your previous posts

http://www.jiskha.com/display.cgi?id=1298862691

Answer 2

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 .