Posted by anon on Monday, February 21, 2011 at 5:25pm.
It is perfectly to repost with a reference to an earlier post.
Here it is:
Given triangle,
A=45-48-36
B=61-02-13
c=426
C=180-00-00 - (45-48-36 + 61-02-13) = 73-09-11
Solve by the sine rule:
a/sin(A)=c/sin(C)
a=c*sin(A)/sin(C)
value logarithm
c 2.6294096
sin(A) 1̅.8555387
c*sin(A) 2.4849483 [ADD]
sin(C) 1̅.9809493
a 2.5039990 [SUBTRACT]
Anti-log 319.1530 (length of c)
Now proceed to calculate area:
Area = (1/2)a*c*sin(B)
value logarithm
(1/2) 1̅.6989700
a 2.5039990
c 2.6294096
sin(B) 1̅.9419744
Area 4.774353 [ADD]
Anti-log 59477.54
Note:
when a number is between 1 and 10, it is normalized, and the logarithm (to the base 10) is between 0 and 1.
Example: log(2) = 0.30103
However, when the number is less than 1, such as 0.5, the decimal is moved one place to the left, and log(5) is recorded (.6989700) with a 1̅ to the left meaning the decimal has been move one to the left.
Conversely, the logarithm of 50 is written simply as 1.6989700, meaning log(5) with one decimal placed to the right.
If you need more details, post (here).
okay i was able to get
c*sin(A)= 1.8555387
but i was lost after that. I couldn't reproduce the same answers u have.
value logarithm
c 2.6294096
sin(A) 1̅.8555387
2.4849483 [ADD]
sin(C) 1̅.9809493
a 2.5039990 [SUBTRACT]
Anti-log 319.1530 (length of c)
Are you able to get the individual logarithms?
For example,
A=45.81°
sin(A)=0.7170323
sin(A)*10=7.170323 (normalize number to between 1 and 10)
Log(sin(A)*10)=0.855387
To move the decimal back one place to the left, we put a (-1) denoted by 1̅ which makes
log(sin(A))=1̅.855387
The we add (instead of multiply) the logarithms
c 2.6294096
sin(A) 1̅.8555387
2.4849483 [ADD]
which is
2.6294096+(-1)+.855387
=2.4849483
Note that the mantissa (the decimal part of the log) is always positive. The characteristics (integer part) are always added separately, and do remember to add the carries, if any.
The subtraction would be calculated similarly.
Please post again if you need more details.