The above formulæ are all that are required for the ordinary solution of plane triangles.

Remarks.—Though such a formula as No. 2 simply mentions A and B and their opposite sides, it holds equally well whether we substitute C for A, or C for B, provided that the sides are changed to correspond also. In Equations 2, 3, 4, and 5, A is intended to represent the greater angle of the two angles A and B.

or, we might equally well have used Eq. 7.

RIGHT-ANGLED TRIANGLES.-In Fig. 99 let A= 90°; then

b and c are of the same species respectively as B and C. Any side is greater than 90° if the other sides are of different species, and less than 90° if of the same species.

B or C is less than 90° if the containing sides are of the same species, and less than 90° if of different species.

Let ABC in Fig. 100 represent any oblique-angled spherical

The greater angle is always opposite the greater side.
No angle or side is greater than 180°.

The sum of any two sides is greater than the third side.
The sum of the three sides is less than 360°.

Given a, b, and C, to find A and B; use Eqs. 2a and 2b.

Miles. Furlongs. Chains. Rods. Yards.

0.00056818 0.0045454 0.045454 0.181818

0.00018939 0.00151515 0.01515151 0.0606060 0.33333 0.000015783 0.000126262 0.001262626 0.00505050 0.0277777 0.083333

1

3

36

1

12

1