 | Henry Raper - Nautical astronomy - 1908 - 1018 pages
...opposite the greater angle. The sum of the three sides of a spherical triangle is less than 360°. The sum of the three angles of a spherical triangle is greater than two right angles and less than six, or always will fall between 180° and 540°. In right-angled spherical... | |
 | Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...> 180° ; and A +B+ C< 540° - 0°, ie A + B+C< 540°. 18. Definitions, a. The amount by which the sum of the three angles of a spherical triangle is greater than 180° is called its spherical excess. It is shown in Art. 57 that the area of a triangle depends upon... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...180° ; and A + B + C< 540° - 0°, ie A + B+C< 540°. 18. Definitions, a. The amount by which the sum of the three angles of a spherical triangle is greater than 180° is called its spherical excess. It is shown in Art. 57 that the area of a triangle depends upon... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Trigonometry - 1910 - 204 pages
...triangle is less than 360°. The triangle may have one, two, or three sides greater than 90°. The sum of the three angles of a spherical triangle is greater than 180°, and less than 540°. The triangle may have one, two, or three angles greater than 90°. If two... | |
 | John Gale Hun, Charles Ranald MacInnes - Trigonometry - 1911 - 234 pages
...measure of the angle A, (page 68 ). Therefore a' + A = 180°, or A = 180° - a', etc. 71. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Let ABC be a spherical triangle. To prove that 180° < A + B + С < 540°. Construct the polar triangle.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...prove that Z C>10°. HINT. Construct the polar A A'B'C'. PROPOSITION XVII. THEOREM 754. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Given ABC, a spherical triangle. To prove ZA + ^B +Zc> 180°, and ^A+ZB+^c< 540°. Proof. Construct... | |
 | Connecticut. Board of Finance and Control - Budget - 1914 - 804 pages
...other as the cubes of their homologous edges (To be proved) 6 Prove — The sum of the angles of any spherical triangle is greater than two, and less than six, right angles 7 Find the lateral area and the volume of a regular quadrangular pyramid whose altitude is 10 and whose... | |
 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...a parallelopiped divides it into two equivalent triangular prisms. 3. (a) Prove that the sum of the angles of a spherical triangle is greater than two, and less than six, right angles. i (b) On a sphere whose radius is 4, given a triangle whose angles are 60°, 65°, and 75° respectively.... | |
 | William Betz - Geometry - 1916 - 536 pages
...congruence theorems for triangles in plane geometry corresponding to all of these cases? 844. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Given the spherical triangle ABC, in which A, B, and C respectively denote the number of degrees in... | |
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The sum of the angles of a spherical triangle is greater than two and less than six right angles. Hyp. ABC is a spherical triangle. To prove ZA + ZB + ZG> 180°, and ZA + ZB + ZC<5±0°. Proof. Construct the polar triangle A'B'C', and denote the number... 
