 | William Smyth - Plane trigonometry - 1852 - 198 pages
...— - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo sides of a triangle is to their difference, as the tangent of...angles is to the tangent of half their difference. parts. Subtracting the angle C 45° from 180°, and dividing the remainder by 2, we have = 67° 30',... | |
 | Benjamin Peirce - Trigonometry - 1852 - 398 pages
...equal to 55° 28' 12" ; to solve the triangle. 81. Tlieorem. The sum of two sides of a triangle is tto their difference, as the tangent of half the sum of...angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1), a : b = sin. A : sin. B ; whence, by the theory of proportions,... | |
 | William Smyth - Navigation - 1855 - 234 pages
...— i— : tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as the tangent of...angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds, BC 70 yds, and the angle C 45° ; it is required to find the... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...BC, or sin. A : sin. B :: BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any tico sides is to their difference, as the tangent of half the...angles is to the tangent of half their difference. Let ABC be any triangle; then will CB+CA : CB-CA : : tang. ^J^ . tan g. ^—? ,--> /-v Produce AC to... | |
 | 1855 - 424 pages
...In any plane triangle, the sum of any tico sides is to their difference as the tangent of half t/ie sum of the opposite angles is to the tangent of half their difference. Let А в о be any triangle ; then will с u с A : с и — OA:: tang. A + B : tang, A — В Produce... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...(2.) In the same way it may be shown that THEOREM II. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin. B : sin. 0 ; hence, by composition and division, we have I +... | |
 | William Somerville Orr - Science - 1856 - 622 pages
...that in any plane triangle, the sum of two tides i> to their difference, at the tangent of half the mm of the opposite angles is to the tangent of half their difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the...angles is to the tangent of half their difference. Let ABC be any triangle ; then will CB+CA : CB-CA : : tang. : tang. Produce AC to D, making CD equal... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...sin ^1 sin £ siu C7° (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the...is to the tangent of half their difference. For, by (90), a : b : : sin A : sin B ; whence (Geom., Prop. XII. Bk. II.), a -\- b : a — b : : sin A -\-... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...B = —-, therefore b = p cot -4, p = b cot 5. 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the...is to the tangent of half their difference. For, by (90), a : 6 : : sin A : sin B; whence (Geom., Prop. XII. Bk. II.), a -\- b : a — b : : sin A -)-... | |
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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. 
