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 Geometry - Page 230by Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1920 - 305 pagesFull view - About this book
| George Roberts Perkins - Geometry - 1860 - 472 pages
...side opposite an acute angle is equal to the sum of the squares of the other two sides, diminished by twice the product of one of these sides, by the projection of the other on the preceding one, produced if necessary. If the angle A is ac,ute, we shall have BC2 = AB2+AC2-2ABxAD.... | |
| 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... | |
| 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... | |
| 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 is the part of the latter intercepted... | |
| Henry Nathan Wheeler - 1876 - 128 pages
...— 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 product of those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC... | |
| 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 product of those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in... | |
| 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 let fall upon... | |
| 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 let fall upon... | |
| Franklin Ibach - Geometry - 1882 - 208 pages
...projection of CD upon AB. -B D ELEMENTS OF PLANE GEOMETRY. THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. equals the sum of...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 Z., and... | |
| Franklin Ibach - Geometry - 1882 - 208 pages
...THEOREM VII. 259. In any triangle, the square on the side opposite an acute anale 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 с be an acute Z., and... | |
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