Plane trigonometry, by S.L. Loney.

190

TRIGONOMETRY.

177. Case III. Given an angle B and one of the sides
a, to solve the triangle.
Here A (= 90 - B) is known. A
The side b is found from the rela- b
tion
= tanB, B a C
and c from the relation
a
- =cosB.
178. Case IV. Given an angle B and the hypothenutse
c, to solve the triangle. A
Here A is known and a and b are c
obtained from the relations b
a b
=cos B, and -= sin B. B C
o a
c c a
EXAMPLES. XXVIII.
1. In a right-angled triangle ABC, where C is the right angle, if
a=50 and B=75~, find the sides. (tan 75~=2+ /3.)
2. Solve the triangle of which two sides are equal to 10 and 50 feet
and of which the included angle is 90~; given that log20= 130103, and
L tan 26033'=9 6986847, diff. for 1'=3160.
3. The length of the perpendicular from one angle of a triangle upon
the base is 3 inches and the lengths of the sides containing this angle are
4 and 5 inches. Find the angles, having given
log 2 =30103, log 3 = '4771213,
L sin 360 52'=9'7781186, diff. for 1= 1684,
L sin 48~ 35'= 9-8750142, diff. for 1'= 1115.
4. Find the acute angles of a right-angled triangle whose hypothenuse
is four times as long as the perpendicular drawn to it from the opposite
angle.