Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch.V] SOLUTION OF RIGHT TRIANGLES BY LOGARITHMS 51
Since angles CBK and CAL=A are both complementary to
angle AKB, they are equal. Hence, from the right triangle BCK,
tanA =tan CK c-b (c-b)2
tan A -tan CBK - b)= = - =
CIKCB a (c+b)(c
by (1). The desired formula is therefore
(2) tanA c-b=
c+b'
In the above example, we had
log (c - b) = 0.4771
log (c + b) = 3.8985
21 4.5786
log tan ~A = 2.2893 = 8.2893 - 10
2A = 1~6.9'.
36. Errors of computation. Gross errors may arise by
1. Reading from the figure the wrong ratio as the value of a
trigonometric function, and hence starting from a false formula.
2. Solving the formula incorrectly for the unknown part.
3. Passing erroneously to the logarithmic form of the formula.
4. Taking an entry from a wrong column of a table, perhaps
using the label at the top instead of the bottom of the column.
5. Failing to omit the characteristic 1 of log a = 1.2470 and
erroneously entering the table with 1247, when seeking a.
6. Adding two logarithms when we should subtract.
7. Supplying the wrong characteristic to the logarithm, perhaps failing to subtract 10 from the tabulated logarithm of a
trigonometric function. When an answer is in error only in the
position of the decimal point, the error was due presumably to the
present cause only.
If wide disagreement with the values from the drawing to scale
or from the traverse table shows that a gross error still remains
undetected, check the additions and subtractions by "casting out
nines." To cast out nines from 678, subtract 9 from 6 + 7 to obtain 4 and subtract 9 from 4 + 8 to obtain 3. To cast out nines