In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle. Plane Geometry - Page 203by John Wesley Young, Albert John Schwartz - 1915 - 223 pagesFull view - About this book
| John Hymers - Trigonometry - 1841 - 151 pages
...also, sin Л а sin B b' It A = 90°, we still have, in conformity with the theorem, 6 sin В = . a 92. **In any triangle, the square of any side is equal to the sum of the** squares of the two other sides, diminished by twice the product of these sides and the cosine of the... | |
| John Hymers - Logarithms - 1858 - 232 pages
...B+ Ъ cos A. \ \ II ii If A = 90° we still have in conformity with the th eorem, с = a cos B. 92. **In any triangle, the square of any side is equal to the sum of the** squares of the two other sides, diminished by twice the product of these sides and the cosine of the... | |
| Benjamin Greenleaf - Geometry - 1862 - 490 pages
...ten|^I^, (94) or, as it may be written, a + b : a — b : : tan £ (A -\- B) : tan £ (A — B). (95) 113. **In any triangle, the square of any side is equal to the sum of the** squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Benjamin Greenleaf - Geometry - 1862 - 490 pages
...£) or, as it may be written, a-\-b : a — b : : tan £ (A + -B) : tan (94) — .B). (95) 113. ./« **any triangle, the square of any side is equal to the sum of the** squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...(A — B) ' « + 6 __ tan % (A + B) tan ^ (A — B) ' (94) (A -\- B) : tan £ (A — B). (95) B 113. **In any triangle, the square of any side is equal to the sum of the** squares of the two other sides, diminished by twice the rectangle of these sides multiplied by the... | |
| Alfred Challice Johnson - Plane trigonometry - 1865 - 150 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
...(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
...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
...— 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 - 208 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... | |
| |