 | English language - 1897 - 726 pages
...the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles opposite is to the tangent of half their difference. That is, a -f J : a — I = tan £ ( A + B) : tan | ( A... | |
 | William Mitchell Gillespie - Surveying - 1897 - 610 pages
...to each other at the opposite sides. THEOREM II. — In every plane triangle, the sum of two tides is to their difference as the tangent of half the sum of the angles opposite those tides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the... | |
 | William Mitchell Gillespie - Surveying - 1897 - 618 pages
...are to each other at the opposite sides. THEOREM II.—In every plane triangle, the turn of two rides is to their difference as the tangent of half the sum of the angles opporite those sides is to the tangent of half their difference. THEOBBM HI.—In every plane triangle,... | |
 | William Kent - Engineering - 1907 - 1206 pages
...triangle — Theorem 1. The sines of the angles are proportional to the opposite sides. Theorem 2. The sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Theorem 3. If from any angle of a triangle... | |
 | Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 242 pages
...42°, C - 116°, a = 564, to find ,4, b, c. 46. In Case 2 we need also The Law of Tangents. In any triangle, the sum of any two sides is to their difference as the tangent of one half the sum of the angles opposite those sides is to the tangent of one half their difference.... | |
 | William Kent - Engineering - 1902 - 1206 pages
...formulas enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin K _ 2 sin \^(A + B) cos J£C4... | |
 | Education - 1903 - 712 pages
...sin x , tan x of the fractions - and - as XX x approaches the limit o. 8. Demonstrate : — In any triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half the difference. GEOLOGY. i. Name the constituents of rocks.... | |
 | William Kent - Engineering - 1902 - 1224 pages
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)... | |
 | James Morford Taylor - Plane trigonometry - 1904 - 192 pages
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of h (1ff their difference. From the law of sines, we have... | |
 | Preston Albert Lambert - Trigonometry - 1905 - 120 pages
...B) Since a and b are any two sides of the triangle, in words the sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half the difference of these angles. The formula a -H1 _ tan £(A... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
