| Aaron Schuyler - Measurement - 1875 - 276 pages
...£(Л + ß) : 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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;... | |
| 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.... | |
| 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,... | |
| 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... | |
| 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 _... | |
| 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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