 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.  Plane and Spherical Trigonometry - 73. lappuseautors: Henry Nathan Wheeler - 1886Pilnskats - Par šo grāmatu
 | Alfred Challice Johnson - 1865 - 166 lapas
...(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 - 1871 - 178 lapas
...(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 lapas
...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 - 1876 - 128 lapas
...— C)' 6 — c tani(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, but PB = PA-fC — — AP-fc (v. § 3, d.) .•.FB2 = AP2 — 2APC + C3, [69] but cos A = — , o .•.... | |
 | Henry Nathan Wheeler - 1876 - 130 lapas
...of half their difference . . 73 § 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... | |
 | Henry Nathan Wheeler - 1877 - 128 lapas
...B) -_tan^ (B-fC) ' ~ ~ — 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...into the cosine of their included angle. FIG. 43. Through c in the triangle ABC (Figs. 43, 44, and 45) draw PC perpendicular to c. In each figure, then,... | |
 | William Frothingham Bradbury - 1877 - 262 lapas
...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... | |
 | Henry Nathan Wheeler - 1878 - 198 lapas
...of half their difference . . 73 § 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 product of those sides into the cosine of Ihoir included angle 73 § 74. Formula for the side of a triangle, in terms of the cosines of the adjacent... | |
 | William Frothingham Bradbury - 1880 - 260 lapas
...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... | |
 | Franklin Ibach - 1882 - 208 lapas
...THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. equals the sum of the squares of the other two sides minus twice the product of one of those sides and the projection of the other upon that side. In the A ABC, let c be an acute... | |
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