Plane trigonometry, by S.L. Loney.

196

TRIGONOMETRY.

B-C
Let then - 240 20 40" ~+".
The difference for = 9'6555845 = 000012.
- 9'655572(
10"= 9'655626[
The difference for 9'655572 000054.
x -000012 2
Hence O- OO5-4 = 9' so that x=2".
B- C
- 24~ 20' 42 "(........................ (1).
B+C A A
But =900- 3=900 37013'30" =52 46'30".......... (2).
2 2
By adding (1) and (2), we have B=77~ 7'12".
By subtracting (1) from (2), we have C=28~ 25' 48".
To get a we have
a c
sin A sin C. log a=log c +L sin A - L sin C
=log 105 + L sin 74~ 27' - L sin 28~ 25' 48"
2-0211893
+ 9-9838052
= 120049945
- 9-6776842
= 2-3273103
= log 212-486.. a= 212-486.
The triangle is therefore completely determined.
183. There are ways of finding the third side a of the triangle in the
previous case without first finding the angles B and C.
Two methods are as follows:
(1) Since a2= b2 + c2- 2bc cos A.
= b2 2 - 2bc (2 cos2- 1)
=(b + c)2 - 4cos
= (b + c)2 - 4be COS2 2 -2'