When two sides are given, to find the angles; then one of the given sides must be made radius.

RULE.

As the side made radius,

Is so radius;

So is the other given side,

To the name upon it.

CASE 1.

The Angles and Hypothenuse given, to find the Legs.

Given, the hypothenuse, 121 perches; the angle, opposite the base, 54° 30'; consequently the other angle, 35° 30', by position 2, page 10.

For the construction, see Problem 10, in Geometry.

By making the Base Radius, it will be,

By making the Perpendicular Radius, it will be,

By making the Hypothenuse Radius, it will be,

BY GUNTER'S SCALE.

All proportions, where secants are not in them, may be worked by Gunter's Scale; the extent from the first to the third term, will reach from the second to the fourth; thus the last radius.

1. Extend from radius 90° to 54° 30', on the line of sines; that extent will reach from the hypothenuse 121, to the base 98.50, on the line of numbers.

2. Extend from radius, to 35° 30', on the line of sines; that extent will reach from the hypothenuse 121, to the perpendicular 70.27, on the line of numbers.

CASE 2 & 3.

The Angles and one Leg given to find the Hypothenuse, and other Leg.

The angle opposite the perpendicular 33° 15', and thebase 274 perches, are given, to find the hypothenuse and perpendicular.

For the construction, see Problem 11, in Geometry.

By making the Base Radius, it will be,

By making the Perpendicular Radius, it will be,