Plane trigonometry, by S.L. Loney.

GIVEN TWO SIDES AND THE INCLUDED ANGLE. 195

Hence tall =1.
2
= 450............................. (1).
B+C A
Also B+_ C =90o _ =90 - 150=75................ (2).
2 2
By addition B = 120~.
By subtraction C= 30~.
Since A = C, we have a=c= 1.
Otherwise. We have
a2= b2+c2 - 2bc cos A= 3 + 1 - 2^/3. =1,
so that a =1 = c.
C. C=A=30~,
and B = 1800 - A - C=120~.
Ex. 2. If b = 215, c= 105, and A = 74~ 27', find the remaining angles,
having given
log 2=30103, log 11 =1-041393,
log 105 = 20211893, log 212-486 = 2-3273103,
L cot 37~ 13' 30" = 10-119341, L tan 24~ 20' 40" = 9-655572,
L tan 24~ 20' 50"= 9-655626, L sin 74~ 27'= 99838052,,and L sin 28~ 25' 48" = 96776842.
B-C b-c A 11
Here tan B - o - cot 37 13' 30".
2 b + c 2 32. L tan B = log 11 - 5 log 2 + L cot 37~ 13' 30"
1-041393 -30103
+ 10-119341 5
11-160734- 1-50515
= 9655584,
so that -2 lies between 24~ 20' 40" and 24~ 20'50".
~2~~~ ~13 -13-2