SOLUTION. Find the side opposite to the other given angle

by Case IV.

CASE VI. Given two angles of an oblique-angled spherical triangle, and a side opposite to one of them, to find the third angle.

SOLUTION. Find the side opposite to the other given angle

by Case IV.

Then, CotA=

tang (C~B)

CASE VII. Given two sides of an oblique-angled spherical triangle, and the angle contained between them, to find the

other angles.

Here b, c, and the included A are given, and formulæ will be obtained by a mere change of letters, if a, b, and the LC; or if a, c, and the B are given.

CASE VIII. Given two sides of an oblique-angled spherical triangle, and the angle contained between them, to find the third side.

SOLUTION. Find the other two angles by Case VII, and then find the third side by Case V.

Or, the sides a, b, or c respectively, may be found by the fourth

set of equations, page 184.

CASE IX. Given two angles of an oblique-angled spherical triangle, and the side adjacent to both of them, to find a side opposite to one of the given angles.

Here A, C and the included side bare will be obtained by a change of letters, if included side c are given; or if LB and side a are given.

given; and formulæ A and B and the C and the included

CASE X. Given two angles of an oblique-angled spherical triangle, and the side adjacent to both of them, to find the other angle.

SOLUTION. Find the other two sides by Case IX, and then find the other angle by Case VI.

Or, I. Cot =

II. Cot =

III. Cot &=

cos a. tang c
rad
cos b. tang A
rad
cos c. tang B
rad

; then, cos Acos c.

sine (B~) sine

; then, cos c=cos B.

sine

Or, the angles A, B, or C, respectively, may be found by the sixth set of equations, page 184.

CASE XI. Given the three sides of an oblique-angled spherical triangle, to find the angles.

SOLUTION. Let a+b+c=s, then

^=rad√sine (§ s

I. Sine Arad t

II. Cos Arad

III. Tang=rad

b). sine (s

sine b. sine c

-c)

sine (s-b). sine (s—c)
sines. sine (s—a)

IV. Cot Arad sine § s . sine († s—a)

sine (s-b). sine (s-c)

II. Cos c=rad sine § s. sine (§ s—c)

sine a. sine b

III. Tang crad

sine (s-b). sine (s-a)
sines. sine ( s—c)

IV. Cotc=rad

sines. sine (s—c)

sine (s-6). sine (s-c)

Or, the angles A, B, or c, respectively, may be found by the formulæ A. 182.

CASE XII. Given the three angles of an oblique-angled spherical triangle, to find the sides.

SOLUTION. Let A+B+C=S, then

COS

cos s cos ( S- - A)

cos s

cos (S-B) sine A sine c

II. Cọt ± b=rad/cos(as−1). cos (as

III. Tangbrad

IV. Cot & b=rad

I. Sinec rad

sine A sine c

c)

Coss. cos (s - B) cos (S-A). Cos (s—c) cos (S-A A). COS (S-C) coss.cos (s-B) cos (s.cos (s—c) sine A sine B

II. Cosc rad

cos (s

A). COS (S-B)

sine A. sine B