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" C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 276 pages
...(Л + ) : tan (Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. We find from the proportion, the equation...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 128 pages
...42, we must remember that sin B is equal to the sine of its supplement CBP. 72. TJte sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. From [67] we get, by the theory of proportions,...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - Trigonometry - 1876 - 226 pages
...sides of auy triangle are proportional to the sines of the opposite angles 72 i 72. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference . . 78 73. The square of any side of...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 pages
...Fig. 42, we must remember that sin B is equal to the sine of its supplement CBP. 72. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of tlie opposite angles is to the tangent of half their difference. From [67] we get, by the theory of...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...proposition, therefore, applies in every case. BOOK Ш. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by (90), a : 6 : : sin A : sin B;...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - Trigonometry - 1876 - 254 pages
...sin В is equal to the sine of its supplement СВP. 72. The sum of any two sides of a triangle ix to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. From [67] we get. by the theory of proportions....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...angles (Art. 53), it follows, from the preceding theorem, that the sura of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This is the same as Theorem II., Art. 54,...
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Elements of Trigonometry: Plane and Spherical

Edward Olney - Trigonometry - 1877 - 220 pages
...horizontal parallax. PLANE TR1GONOMETRY. 86. Prop.— The sum of any two sides of aplane triangle 's to their difference, as the tangent of half the sum of the angles oppos'te is to the tangent of half their difference. DEM. — Letting a and b represent any two sides...
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The Elements of Plane Trigonometry

Eugene Lamb Richards - Plane trigonometry - 1878 - 134 pages
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA _...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

Surveying - 1878 - 534 pages
...to each other at the opposite sides. THEOREM IL—In every plane triangle, the sum of two tides it to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of kalf their difference. THEOKEJI III.—In every plane triangle,...
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