 The square of any side of a triamjle is equal to the sum of the squares of the other two sides diminished by twice their product into the cosine of the included angle. • SECTION XXXVI LAW OF TANGENTS By Sect. XXXIV, p. 64, a : b = sin A : sin B...  Five-place Logarithmic and Trigonometric Tables - Page 64by George Albert Wentworth, George Anthony Hill - 1903 - 75 pagesFull view - About this book
 | Benjamin Peirce - Trigonometry - 1852 - 410 pages
...proportions, a -f- b : a — b = sin. A -\- sin. B : sin. A — sin. B, which, expressed fractionally, is a -\- b _ sin. A -\- sin. B a — b sin. A — sin. B' But, by (47), I sin. A -j- sin. B _ tang. ¿ (A -f- B) sin. A — sin. B tang. f¡ (A — B) ' whence a —... | |
 | Benjamin Peirce - Trigonometry - 1852 - 398 pages
...-j- b : a — b — sin. A -f- sin. B : sin. A — sin. B, which, expressed fractionally, is a -f- b _ sin. A -\- sin. B a — b sin. A — sin. B ' But, by (47), sin. A -f- sin. B tang. ¿ (A -\- B) sin. A — sin. B tang. J (A — B) ' whence а + b = tang.... | |
 | Benjamin Peirce - Plane trigonometry - 1861 - 394 pages
...+ c2 — 2 Jccos. A; (139) that is, Йе square of either side of a triangle is equal to the sum of the squares of the other two sides diminished by twice their product multiplied by the cosine of the included angle. 87. Corollary. The above proposition, when applied... | |
 | George Albert Wentworth - Trigonometry - 1882 - 234 pages
...twice the product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, a : b = sin A : sin B ; whence, by the Theory of Proportion, a — b _ sin A — sin B a -f- b sin A + sin B But by [24], page 48, sin A — sin B _ tan \ (A — B) sin A + sin B tan J (A... | |
 | George Albert Wentworth - Trigonometry - 1882 - 160 pages
...the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By §36, a: b = smA : sin.5; whence, by the Theory of Proportion, a — b _ sin A — sin B a-\-b sin A + sin B But by [24], page 48, sin A — sin B _ tan í (A — B) sin A + sin B ~~ tan i... | |
 | George Albert Wentworth - 1887 - 346 pages
...sides and the cosine of the included angle. § 38. LAW OF TANGENT8. By § 36, a : b = einA : sinJS; whence, by the Theory of Proportion, a — b _ sin A — sin B a + b sin .4 + sin JS But by [24], page 48, sin A — sin B _ tan j (A — 7?) sin A + sin B ~ tan \(A + B) Therefore,... | |
 | George Albert Wentworth - Surveying - 1889 - 280 pages
...the product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, а : b = sin A : sin B ; whence, by the Theory of Proportion, a — b _ sin A — sin Б a-\-b sin A + sin Б But by [24], page 48, sin A — sin Б _ tan \ (A — B) ~ Therefore, a-b_tani(AB)... | |
 | George Albert Wentworth - Surveying - 1890 - 186 pages
...twice the product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, a : b = sin A : sin B ; whence, by the Theory of Proportion, a — b _ sin A — sin B a-\-b sin A + sin B But by [24], page 48, sin A — sin B _ tan j ( A — £} sin A + sin ^"tan* (A... | |
 | George Albert Wentworth - Surveying - 1891 - 286 pages
...product of the sides and the cosine of the included angle, § 38. LAW OF TANGENTS. By § 36, а : Ь = sin A : sin B ; whence, by the Theory of Proportion, a — b _ sin A — sin В a + b sin A + sin В But by [24], page 48, sin A — sin В _ tan í (A — B) sin A + sin В -... | |
 | George Albert Wentworth - Navigation - 1892 - 372 pages
...product of the sides and the cosine of the included angle. § 38. LAW OF TANGENTS. By § 36, a:b = sin A : sin B ; whence, by the Theory of Proportion, a — b _ sin A — sin B a-\-b sin A -\- sin B But by [24], page 48, sin A — sin B _ tan £ (A — B] ~ Therefore, a — b_tanKA-B)... | |
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