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Any angle is greater than the difference between 180° and the sum of the other two angles.
Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ... - Pągina 144
per Aaron Schuyler - 1864 - 490 pągines
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## First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 71 pągines
...Ans. a = 53° 10', b= 4°, с = 53° 8'. / Л . (822) 71. Theorem. Each angle of a spherical triangle is greater than the difference between 180° and the sum of the other two angles. Demonstration. Since sin. В and sin. С are posi(823) tive, the denominator of the fraction...
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## First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 71 pągines
...89°, B = 5°, С = 88° ; to solve the triangle. (822) 71. Theorem. Each angle of a spherical triangle is greater than the difference between 180° and the sum of the other two angles. Demonstration. Since sin. B and sin. C are posi(823) tive, the denominator of the fraction...
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## An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 449 pągines
...Each side is less than the sum of the other two. III. The sum of the sides is less than 360°. IV. Each angle is greater than the difference between 180°, and the sum of the other two angles. There are, however, cases in which these conditions are all satisfied by each of the values...
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## An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 449 pągines
...Each side is less than the sum of the other two. III. The sum of the sides is less than 360°. IV. Each angle is greater than the difference between 180°, and the sum of the other two angles. There are, however, cases in which these conditions are all satisfied by each of the values...
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## A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852
...two. III. The sum of the sides is less than 360°. IV. The sum of the angles is greater than 180°. V. Each angle is greater than the difference between 180° and the sum of the other two angles. For, by IV., A + B + С> 180° whence, A > 180° - (B + C) But if B + C> 180°, we have,...
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## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 pągines
...is greater than 180°. IV. Ttie greater side is opposite the greater angle, and conversely. V. Any angle is greater than the difference between 180° and the sum of the other two angles. VI. A side which differs more from 90° than another side, is of the same species as its...
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## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 pągines
...angles is greater than 180°. IV. The greater side is opposite the greater angle, and conversely, V. Any angle is greater than the difference between 180° and the sum of the other two angles. VI. A side which differs more from 90° than another side, is of the same species as its...
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## Catalogue - Harvard University

1874
...sides, and what term is applied to the triangle* ? 11. Prove that eiioh angle of a spherical triangle is greater than the difference between 180° and the sum of the other two. 12. The height ot'a right cylinder is equal to the diameter of the base. What is the ratio of...
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## Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 184 pągines
...greater than 180°, and less than 540 \ 6. Each angle æs greater than the difference between 180° ana the sum of the other angles. For, A + B + C > 180°....the polar triangle, we have, by principle 3. a' < b' + c'. or 180° — A < 180° — B + 180° — C. or — A < I8O' — (B + C). .-. A > B + 17—180°....
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## Plane and Spherical Trigonometry

Henry Nathan Wheeler - 1876 - 208 pągines
...two. k. The sum of the sides is less than 360°. L The sum of the angles is greater than 180°. m. Each angle is greater than the difference between 180° and the sum of the other two angles. n. A side which differs more from 90° than another side is in the same quadrant as its...
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