NOTE. Wentworth & Hill's Five-place trigonometric and logarithmic tables have full explanations, and directions for using them. Before proceeding to Chapter II. the student should learn how to use these tables.

Table VI. is to be used in solutions without logarithms. This fourplace table contains the natural functions of angles at intervals of 1′. The decimal point must be inserted before each value given, except where it appears in the values of the table.

CHAPTER II.

THE RIGHT TRIANGLE.

§ 10. THE GIVEN PARTS.

In order to solve a right triangle, two parts besides the right angle must be given, one of them at least being a side. The two given parts may be:

I. An acute angle and the hypotenuse.

II. An acute angle and the opposite leg. III. An acute angle and the adjacent leg. IV. The hypotenuse and a leg.

V. The two legs.

§ 11. SOLUTION WITHOUT LOGARITHMS.

The following examples illustrate the process of solution when logarithms are not employed.

§ 12. GENERAL METHOD OF SOLVING THE RIGHT TRIANGLE.

From these five cases it appears that the general method of finding an unknown part in a right triangle is as follows:

Choose from the equation A+B=90°, and the equations that define the functions of the angles, an equation in which the required part only is unknown; solve this equation, if necessary, to find the value of the unknown part; then compute the value.

NOTE. In Case IV., if the given sides (here a and c) are nearly alike in value, then A is near 90°, and its value cannot be accurately found from the tables, because the sines of large angles differ little in value (as is evident from Fig. 4). In this case it is better to find B first, by means of a formula proved later. See formula [18], § 30; viz.,