THE erection of a perpendicular by the construction of a triangle whose sides are respectively 3, 4 and 5 units in length is a familiar and handy device. The following table gives a greater range of choice in the shape or proportions of the triangle employed. The table is a list of all integral, or whole-number, right-angled triangles the units of whose least sides do not exceed 20. To construct any angle from the table of chords, page 282: Let the required angle be 36° 38'; the nearest angles in the table are 36° 30' and 36° 40′, and the chords are respectively 0.6263 and 0.6291, the difference 0.0028 corresponding to an angular difference of 10'. To find the amount which must be added to 0.6263 (the chord corresponding to 36° 30') in order to obtain the chord for a 36° 38′ arc, multiply 0.0028 by fo 0.00224. 0.6263 + 0.00224 0.62854. Then, if the radius is 1" and the angle 36° 38′ the chord will be 0.62854". = In laying out an angle as in the accompanying illustration a base line A B can be drawn, say 10 inches long, then with a radius A B and center A, arc B C can be struck. Multiply chord 0.62854 inch by 10 giving 6.2854 inches, as the radius of an arc to be struck from center B and cutting arc B C at C. Through point C draw a line A C and the angle B A C will equal 36° 38'. Where the angle required is in even degrees or sixths of degrees (as ro', 20', etc.) the corresponding chord may be taken directly from the table. A 10 to 1 layout is particularly convenient as the multiplication of the tabulated chords by 10 is readily performed mentally. |