 In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.  The Elements of Plane Trigonometry - Page 73by Henry Nathan Wheeler - 1878 - 112 pagesFull view - About this book
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...(A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the angle included by them. First, let the triangle А В С be acute... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...(А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the anale included by them. First, let the triangle А В С be acute... | |
 | André Darré - 1872 - 226 pages
...H THEOREM. 91. In any triangle the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides by the projection on it of the other. Def. The projection of one line on another... | |
 | Henry Nathan Wheeler - 1886 - 250 pages
...manner — C) r _ ' a' b — c~~ § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the...draw PC perpendicular to c. In each figure, then, a 2 = PB2 -f- pc2, but PB = PA + A« = — AP -f- c (y. § 3, d.) .'. PB2=AP2 — 2 APC-|-C", but cos... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 218 pages
...of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice (he product of those sides into the cosine of their included...draw PC perpendicular to c. In each figure, then, FIG. 45. a = PB pc2, but PB = PA -|- AB = — AP -f- c (v. § 3, d.) .-. a2=PC2-|-AP2-|-C2 — 2APC,... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 254 pages
...— C)' 6 — c~taní (В — С)' § 73. The square of any side of a triangle is equal to che sum of the squares of the other two sides. minus twice the...cosine of their included angle. FIG 43. FIG 44. Through с in the triangle ABC (Figs. 43, 44. and 45) draw PC perpendicular to c. In each figure. then. but... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...of half their difference . . 78 § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the...those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in terms of the cosines of the adjacent angles and the... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...XXVIII. 68. In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular... | |
 | Henry Nathan Wheeler - 1876 - 246 pages
...<v§ 73. The square of any side of a trianrjle is equal to the sum of the squares of the other tico sides, minus twice the product of those sides into the cosine of their included angle. FIG. 43. F'G- **. Through с iu the triangle ABC (Figs. 43, 44, and 45) draw PC perpendicular to c. In each... | |
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