| 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 - 1204 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 - History - 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... | |
| |