 | James Hann - 1854 - 138 pàgines
...+ b tan By Art. 19, —jjHence the following rule : As the sum of any two sides of a plane triangle is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference. By Art. 16, .-. a2 - o2 = c2 - 2bc cos... | |
 | John Radford Young - 1855 - 218 pàgines
...and this proportion expressed in words is the following rule. RULE. As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. that is 0-6 (1) Two sides of a triangle are... | |
 | William Somerville Orr - 1856 - 622 pàgines
...difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their difference, So is the tangent of half the sum of the opposite angles To the tangent of half their difference. The half difference of the unknown angles... | |
 | W. Davis Haskoll - 1858 - 422 pàgines
...When the three given parts are two sides and the included angle. — As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. In the triangle ABC, AB = 345, and BC = 174,... | |
 | William Thomas Read - 1862 - 144 pàgines
...angle, to find the rest. Proposition HI. may here be written as a rule. " As the sum of the given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. And the half difference added to half the... | |
 | Olinthus Gregory - 1863 - 482 pàgines
...the tangent of the sum or difference of the arcs. 11. As the sum of the sines of two unequal arcs, is to their difference ; so is the tangent of half the sum of those two arcs to the tangent of half their difference. 12. Of any three equidifferent arcs, it will... | |
 | Samuel Alsop - 1865 - 440 pàgines
...180° : the remainder will be the sum of the remaining angles. Then, As the sum of the given sides is to their difference, so is the tangent of half the sum of the remaining angles to the tangent of half their difference. This half difference added to the half sum... | |
 | William Davis Haskoll - 1868 - 252 pàgines
...angle will be acute. When two sides and their included angle are given. — As the sum of any two sides is to their difference, So is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
 | William Thomas Read - 1869 - 176 pàgines
...DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ... | |
 | Horatio Nelson Robinson - 1875 - 288 pàgines
...sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between D and... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
