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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 169
by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pages

Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - Mathematics - 1918 - 344 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. 0 Outline of proof. Let ZB be the given obtuse...

Plane Geometry: I. Abridged and Applied. II. College Preparatory

Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 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 upon that side. Show very briefly how to construct a triangle having given the base, the projections...

Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...331. In an obtuse-angled triangle the square of the side opposite the obtuse angle equals the sum of the squares of the other two sides plus twice the product of one of these sides by the projection of the other side upon it. A B Given the triangle ABC, in which AK is...

Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...and 340 can be grouped under one statement: The square of one side of a triangle equals the sum of the squares of the other two sides plus twice the product of one of those sides and the external projection of the other upon it. Thus if we draw an obtuse triangle, we have Art. 340. If...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 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 6 upon c, and the angle opposite a an acute angle. To prove a2 = 62 +...

Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...acute •angle of any triangle 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. BA Given the A ABC with an acute ZA, and a' and V, the projections of a and 6 respectively upon c....

Plane Geometry: (Revised)

Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 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...the other side upon it. Given the obtuse triangle ACB, with angle ACB obtuse, and a' and c' the projections of a and c, respectively, upon the side 6....

Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...angle of any obtuse triangle 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 side upon it. 12. The sum of the squares of two sides of a triangle is equal to twice the square of half the third...