Plane trigonometry, by S.L. Loney.

180

TRIGONOMETRY.

[Exs. XXVI.l

2. Given a=125, b = 123 and c = 62,
find the sines of half the angles and the sines of the angles.
3. Given a=18, b=24 and c=30,
find sin A, sin B, and sin C.
4. Given a=35, b=84 and c=91,
find tan A, tan B, and tan C.
5. Given a=13, b=14 and c=15,
find the sines of the angles.
6. Given a=287, b=816 and c=865,
find the values of tan A and tan A.
2
7. Given a==V3, b =/2 and c = '2
find the angles.
170. In any triangle to prove that
a = b cos C - c cos B.
Take the figures of Art. 164.
In the first case, we have
BD
B = cosB, so that BD = c cos B,
BA
CTD
and CA =cos C, so that CD = b cos C.
Hence a = BC= BD + DC = c cos B + b cos C..
In the second case, we have
BD
= cos B, so that BD = c cos B,
BA
CD
and A = cos A CD = cos (180~ - C)
GA
=- cos C (Art. 72),
so that CD =- b cos C.