| William Mitchell Gillespie - Surveying - 1897 - 592 pages
...angles are to each other a& the opposite sides. THEOREM II. — In every plane triangle, the sum of **two sides is to their difference as the tangent of half the sum of the angles** opposite those sides is to the tangent of half their difference. THEOREM III. — In eve.ry plane triangle,... | |
| 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) :... | |
| 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 - 258 pages
...116°, a = 564, to find Л, f), 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... | |
| 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... | |
| James Morford Taylor - Trigonometry - 1905 - 256 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 half their difference. From the law of sines, we have By... | |
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