| William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is **the tangent of half the sum of the angles at the base to the tangent of half** their difference. 4. In any plane triangle, as the cosine of half the difference of the angles at the... | |
| Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...no difference, provided the right order is maintained. 97. Law of Tangents. — 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 their difference. By Art. 95, a : b = sin A : sin B. By composition... | |
| Edward Albert Bowser - Trigonometry - 1892 - 196 pages
...no difference, provided the right order is maintained. 57. Law of Tangents. — 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 their difference. By Art. 55, a : b = sin A : sin B. By composition... | |
| Education - 1892 - 754 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle **is to their difference as the tangent of half the sum of the** two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms... | |
| Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...Л. jj .-. CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, in any plane 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 their difference. Scholium. — The half difference added... | |
| Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...(3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of **two sides is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin... | |
| Webster Wells - Trigonometry - 1896 - 236 pages
...manner, b : с = sin B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ 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 their difference. By (47), a : b = sin A : sin B. Whence... | |
| William Mitchell Gillespie - Surveying - 1896 - 594 pages
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u **to their difference as the tangent of half the sum of the angles** opposite those sides is to the tangent of half their difference. TE1EOBEM III. — In every plnne triangle,... | |
| Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...Two Sides and the Included Angle (b, c, a) . First Method. — 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 their difference. For we have b _ sin ß с sin y By composition... | |
| William Chauvenet - Geometry - 1896 - 274 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =... | |
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