Plane trigonometry, by S.L. Loney.

192

TRIGONOMETRY.

The angle A may also be obtained from the formula
b2 __ ~2 _ a2
cos A = 2 (Art. 164.)
This formula is not, in general, suitable for logarithmic
calculation. It may be conveniently used however when
the sides a, b, and c are small numbers.
Ex. The sides of a triangle are 32, 40, and 66 feet; find the angle
opposite the greater side, having given that
log 207=2-3159703, log 1073=3-0305997,
L cot 66~ 18'= 9-6424341, tabulated difference for 1'= 3431.
Here a=32, b=40 and c=66,
32 ~ 40 + 66
so that s-= 69, s - a= 37, s - b = 29 and s - c = 3.
2
ence cot = s (s - c) 69x3 / 207
Hence (s-a (-b) - 37 x 29 1073
C 1
cot = 10 + [log 207 - log 1073]
2 2
= 10 + 1 15798515 - 1-51529985
= 9-6426853.
L cot - is therefore greater than L cot 66~ 18',
2
so that C is less than 66~ 18'.
Let then -= 66 18' - x".
The difference in the logarithm corresponding to difference of x" in the
angle therefore
= 96426853
- 96424341
= 0002512
Also the difference for 60"= 0003431.
x -0002512
Hence
~~~~Hence 60 = 0003431'
2512
so that x = 3 x 60 =nearly 44.
3 43 1
C- 660 18/- 44"/=66 17' 16", and hence C= 1320 34' 32".
2 -