| Geometry, Plane - 1911 - 192 pages
...Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of **the squares of the other two sides diminished by twice the product of one of** these sides and the projection of the other upon that side. 4. Prove that regular polygons of the same... | |
| William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...THEOREM 420. 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...one of those sides and the projection of the other** upon it. FIG. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side b upon the... | |
| William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...THEOREM 420. 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...one of those sides and the projection of the other** upon it. FIG. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side b upon the... | |
| Arkansas Education Association - Education - 1912 - 270 pages
...theorem, "In any oblique 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** two sides and the projection of the other one on that one." When we come to this theorem we know already... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...as follows : 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** these sides and the projection of the other side upon it. Ex. 726. If the sides of a triangle are 7,... | |
| George Clinton Shutts - Geometry - 1912 - 392 pages
...side opposite an obtuse angle of a triangle equals the sum of the squares of the two other sides plus **twice the product of one of those sides and the projection of the other** upon it. Given a A with sides a, b, c, side a being opposite an obtuse angle, and m being the projection... | |
| George Clinton Shutts - Geometry - 1912 - 392 pages
...side opposite an acute angle of a triangle equals the sum of the squares of the two other sides minus **the product of one of those sides and the projection of the other** upon it. Given a A with the sides a, b, c, side a being opposite an acute angle and m being the projection... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...XXXVI. THEOREM 331. 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...side upon it. Given in A abc, p the projection of** 6 upon c, and the angle opposite a an acute angle. To prove a2 = 62 + <? — 2 cp. Proof. Denote the... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...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....the projection of b upon c, and the angle opposite a** obtuse. To prove a 2 = ft 2 + c 2 + 2 cp. Proof. a 2 = A 2 + (c + p) 2 . But /i 2 = 6 2 -p 2 . Ex.... | |
| Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...any triangle the square on the side opposite the acute angle is equal to the sum of the squares on **the other two sides diminished by twice the product...one of those sides and the projection of the other** upon it. Given the A ABC in which C is an acute angle. Let a, b, c be the sides opposite the angles... | |
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