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" 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. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 190
1898 - 208 pages
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...any triangle, the square on the side opposite an acute angle is equal to the sum of the squares on the other two sides minus twice the product of one of these sides and the projection of the oiher sule upon it. AA Given : A ABC, an acute ZC, and the projection DC of AC on BC. To Prove : AB2...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 206 pages
...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. Draw A ABC having an obtuse angle at C; draw AD _L BC, meeting BC extended at D. We then have : Given...
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Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...formulas can be expressed in words : 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 multiplied by the cosine of their included angle. NOTE. In Fig. 49 a, A is acute and...
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Exercises in Geometry

Grace Lawrence Edgett - Geometry - 1909 - 104 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 these sides and the projection of the other upon that side. 11. DE is a line parallel to AB, the hypotenuse of the right triangle ABC, meeting...
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Plane Trigonometry

Edward Rutledge Robbins - Logarithms - 1909 - 184 pages
...sin A sin B sin С 75. LAW OF COSINES. In any triangle the square of one side |g equal to the sum of the squares of the other two sides minus twice the product of these two sides times the cosine of their included angle. Given : A ABC whose sides are a, o, e. /...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...I. 437. THEOREM. Tlie square of a side opposite an acute angle of a triangle is equal to the sum of the squares of the other two sides minus twice the...one of these sides and the projection of the other upon it. om Outline of Proof : In either figure let ZB be the given acute angle, and in each case BD...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...I. 437. THEOREM. The square of a side opposite an acute angle of a triangle is equal to the sum of the squares of the other two sides minus twice the...one of these sides and the projection of the other upon it. CC cm Outline of Proof : In either figure let ZB be the given acute angle, and in each case...
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Secondary-school Mathematics, Volume 2

Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...XLVIII 195. 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...sides and the projection of the other side upon it. Draw A ABC, either acute-angled or obtuse-angled at B. Draw CE.LAB. Then AE (p) is the projection of...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 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 these sides and the projection of the other side upon it. A Given A BAX with ZX obtuse, and p, the projection of b upon a. To prove a? = of + b2 + 2 op. 1. 2....
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Secondary-school Mathematics, Book 2

Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...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 190 Polygons THEOREM XXXIII 149. The sum of the angles of any polygon is equal to twice as many right...
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