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 diminished by twice the product of one of those sides and the projection of the other side upon it. Plane and Solid Geometry - Page 169by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pagesFull view - About this book
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...— In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of **the squares of the other two sides plus twice the...one of those sides and the projection of the other** upon it. Y~ Hypothesis. In A ABC, ZA is obtuse, a, b, and c are the sides opposite A, B, and C, respectively,... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...side opposite an acute angle is equal to the sum of the squares on the other two sides, diminished by **twice the product of 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 have c2 = h2... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...side opposite an acute angle is equal to the sum of the squares on the other two sides, diminished by **twice the product of 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 have c2 = h2... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...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 those sides and the projection of the other** upon it. DB Hypothesis. — In A ABC, Z. A is acute, a, b, and e are the sides opposite A, B, and (7,... | |
| Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...triangle having an obtuse angle, the square of the side opposite the obtuse angle is equal to the sum of **the squares of the other two sides, plus twice the product of one of** these sides and the projection of the other side upon it. A a Hypothesis. In A ABC, ZC is an obtuse... | |
| William Betz - Geometry - 1916 - 536 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by **twice the product of one of those sides and the projection of the other** upon it. Given, in the triangle ABC, that p is the projection of the side b upon the side a, and that... | |
| Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...side opposite the 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** A other upon it.) FIG. 79 Since b' = b cos A, it follows that a2 = b2+c2-26c cos A. This means that... | |
| Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...In any obtuse triangle, the square of the side opposite the obtuse angle is equivalent to the sum of **the squares of the other two sides, plus twice the...sides and the projection of the other side upon it.** § 381. Theorem. In any triangle, the square of a side opposite an acute angle is equivalent to the... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 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 those sides and the projection of the other side upon it. Given** in A abc, p the projection of b upon c, and the angle opposite a an acute angle. To prove a2 = ft2... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...376. THEOREM. The square of the side opposite an obtuse angle of a triangle is equal to the sum of **the squares of the other two sides plus twice the product of one of** these sides and the projection of the other upon it. Outline of proof. Let ZB be the given obtuse angle... | |
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