 | Harvard University - 1873 - 732 pages
...proportional to the sines of the opposite angles. (4.) The sum of any two sides of a plane triangle ia to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 4. Two sides of a plane oblique triangle... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...have tl1e following principle : In any plane triangle, the sum of the sides including either angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. The half sum of the angles may he found... | |
 | William Hamilton Richards - 1875 - 216 pages
...given angle from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347 Log.... | |
 | Cornell University - 1875 - 1012 pages
...cos'^r — sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal... | |
 | Aaron Schuyler - Measurement - 1875 - 284 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... | |
 | William Mitchell Gillespie - Surveying - 1875 - 530 pages
...each other as THEOREM II— In every plane triangle, the sum of two sides is to their difference us the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM ILL— In every plane triangle, the cosine of any... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...The 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
...sides of any triangle are proportional to the sines of { 72. The surn 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
...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... | |
 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1877 - 488 pages
...from a given point, find the distance of each from the given point. 2. In a plane triangle, prove that the sum of two sides is to their difference, as the tangent of J the sum of the angles opposite them is to the tangent of J their difference. 3. Prove: tan. a=- sln... | |
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In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. 
