| Public schools - 1878 - 710 pages
...comes to rest ? TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure **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. 2. Give the limiting values of the circular... | |
| 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, the... | |
| 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 _... | |
| Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...then also Sin. B AC Sin. C~AB' For, since C is a right angle, its sine is 1 (Art. 35). Also 49. In any **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. Let ACB be any triangle. Then BC+CA _ tan.... | |
| Michael McDermott - Civil engineering - 1879 - 552 pages
...two Sida and their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the **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 ; ¿ «., a -f Ъ : a — b : : tan. J (A... | |
| Elias Loomis - 1880 - 456 pages
...supplement of ABC, their sines are equal, Art. 13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. Let ABC be any triangle ; then will CB... | |
| Nautical astronomy - 1880 - 880 pages
...any triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the **sides is to their difference as the. tangent of half the sum of the angles** at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle ABC,... | |
| James Edward Oliver - Trigonometry - 1881 - 120 pages
...negative, according as it is measured in a positive or negative direction from the origin used. Tнм. 2. **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tan¿(A... | |
| Cornell University. Department of Mathematics - 1881 - 120 pages
...negative, according as it is measured in a positive or negative direction from the origin used. Тнм. 2. **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~b) = tan ¿(A... | |
| Education - 1883 - 748 pages
...of 45°. 4. Give directions for finding the logarithm of a number having four places. 5. Show that **in any plane triangle the sum of any two sides is...their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. GENERAL HISTORY. 2. What colonies were... | |
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