Plane trigonometry, by S.L. Loney.

194

TRIGONOMETRY.

181. Case II. Given two sides b and c and the
included angle A.
Taking b to be the greater of the two given sides,
we have A
tan 2 =b+ccot A(Art. 171.(),
1 2 2
and BC 90~-A (2). B/ — \
These two relations give us
B-C B+C
-2 and 2 '
and therefore, by addition and subtraction, B and C.
The third side a is then known from the relation
a b
sin A sin B'
sill A
which gives a = bsin A
sin B'
and thus determines a.
The side a may also be found from the formula
a2 = b + c - 2be cos A.
This is not adapted to logarithmic calculation but is
sometimes useful, especially when the sides a and b are
small numbers.
182. Ex. 1. If b= /3, c=1, and A =30~, solve the triangle.
We have
B-C b-c A V/3 - 1
tan — 2 cot- cot 15
2 b+c 2 /3-+1
Now tan 150^/3-1 (Art. 101),
3o 1 + 1
so that cot 15~ —/3 +
/3-1'