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 diminished by twice the product of one of those sides and the projection of the other upon that side. Elements of Plane and Solid Geometry - Page 188by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...AB*. PROPOSITION XI. THEOREM 341. In any triangle the square on the side opposite an acute angle is **equivalent to the sum of the squares on the other two sides diminished** l by twice the product of one of those sides by the projection of the other upon that side. a CD B... | |
| Robert Édouard Moritz - Trigonometry - 1913 - 560 pages
...embody the so-called Law of Cosines: In any triangle, the square on any side is equal to the sum of **the squares on the other two sides diminished by twice the product of** those two sides times the cosine of the included angle. (b) Second proof. The law of cosines may be... | |
| Herbert Ellsworth Slaught - Logarithms - 1914 - 398 pages
...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 diminished by twice the product...sides and the projection of the other upon that side.** Theorem 2. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the... | |
| Ernest Julius Wilczynski - Plane trigonometry - 1914 - 296 pages
...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 diminished by twice the product...sides and the projection of the other upon that side.** Theorem 2. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the... | |
| Charles Sumner Slichter - Functions - 1914 - 516 pages
...square of any side opposite an acute angle of an oblique triangle is equal to the sum of the squares of **the other two sides diminished by twice the product of one of those sides** by the projection of the other side on it. Thus in Fig. 119 (1) : o2 = 62 _|_ C2 _ 2bd (1) Now: d =... | |
| Wallace Alvin Wilson - Geometry, Analytic - 1915 - 232 pages
...the side opposite an acute angle is equal to the sum of the squares of the other two sides decreased **by twice the product of one of those sides and the projection of the other upon** it ; (б) the sum of the squares of two sides is equal to twice the square of one half the third side,... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 336 pages
...side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, plus **twice the product of one of those sides and the projection of the other** side upon it. Given the obtuse triangle ABC, the angle ACB being obtuse, and d and AD being the projections... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...119. Theorem XI. In any triangle the square on the side opposite an acute angle is equal to the sum of **the squares on the other two sides, diminished by...one of those sides and the projection of the other** side upon it. Give the proof of this on the same plan as in the preceding theorem, noting that we now... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...119. Theorem XI. In any triangle the square on the side opposite an acute angle is equal to the sum of **the squares on the other two sides, diminished by...one of those sides and the projection of the other** side upon it. Give the proof of this on the same plan as in the preceding theorem, noting that we now... | |
| William Betz - Geometry - 1916 - 536 pages
...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 diminished by twice the product...of those sides and the projection of the other upon** it. FH;. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side 6 upon the side... | |
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