 | Andrew Duncan (Surveyor) - Surveying - 1854 - 156 pages
...their included angle are given to find the other angles and side. RULE. — As the sum of the sides is to their difference so is the tangent of half the sum of the opposite angles to the tangent of half the difference ; this half difference added to half the sum... | |
 | James Hann - Plane trigonometry - 1854 - 138 pages
...+ b tan By Art. 19, —jjHence the following rule : As the sum of any two sides of a plane triangle is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference. By Art. 16, .-. a2 - o2 = c2 - 2bc cos... | |
 | Allan Menzies - 1854 - 520 pages
...be given, then rule is, — Sum of the two sides (containing given angle) is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle C), then having found... | |
 | John Radford Young - 1855 - 218 pages
...and this proportion expressed in words is the following rule. RULE. As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. that is 0-6 (1) Two sides of a triangle are... | |
 | William Somerville Orr - Science - 1856 - 622 pages
...difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their difference, So is the tangent of half the sum of the opposite angles To the tangent of half their difference. The half difference of the unknown angles... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 pages
...TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the two sides, CA and... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...When the three given parts are two sides and the included angle. — As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. In the triangle ABC, AB = 345, and BC = 174,... | |
 | Euclides - 1860 - 288 pages
...of half their difference. 13. The base of a triangle is to the difference of its sides, as the sine of half the sum of the angles at the base to the sine of half their difference. 14. The base of a triangle is to the difference of its segments, as... | |
 | Alfred Wilks Drayson - 1861 - 236 pages
...proceed as follows : — Suppose AB, BC, known, and the angle ABC. Then as the sum of the two sides Is to their difference, So is the tangent of half the sum of the two unknown angles To the tangent of half their difference. Half their difference thus found, added... | |
 | War office - 1861 - 714 pages
...triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart find the angles... | |
| |
AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
