| 1853 - 476 pages
...each other as the sides opposite. 5. Find the value of tang. (a+b). 6. In a plane triangle, show that **the sum of two sides is to their difference as the tangent of half the sum** is to tangent of half the difference of the angles opposite. 7. Find the sin. \ A, and prove that 1... | |
| Jeremiah Day - Mathematics - 1853 - 5 pages
...therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, **is to their difference ; as the tangent of half the sum of** tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to... | |
| Allan Menzies - 1854
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) **is to their difference as the tangent of half the...the base is to the tangent of half their difference** ; half the sum = ^ (180 — angle C), then having found the half sum, J sum + £ diff. = greater angle,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...sides. 90. We also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any **two sides is to their difference, as the tangent of half the sum of the** opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,... | |
| Charles Davies - Navigation - 1854 - 444 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, **is to their difference, as the tangent of half the sum of the** two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC... | |
| William Mitchell Gillespie - Surveying - 1855 - 436 pages
...triangle, the sines of the angles are to each other as 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 every plane triangle,... | |
| William Smyth - Navigation - 1855 - 236 pages
...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 half the sum of the** opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
| James Pryde - Navigation - 1867 - 458 pages
...add the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the **sides is to their difference as the tangent of half the sum of the** remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
| Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 288 pages
...tang } (A — B) Therefore, a + I _ tang } (A + B) a — b tang} (A — B) *• ; which shows that, **in any triangle, the sum of two sides is to their...difference as the tangent of half the sum of the angles** opposite to those sides is to the tangent of half their difference. We have A + B=180° — C; hence... | |
| William Mitchell Gillespie - Electronic book - 1868 - 530 pages
...triangle, the sines of the angles are to each other as 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 every plane triangle,... | |
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