This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ....B' = 180--J3, C" = 180--(A+B')=B--A, a sin C c' =--.--j--Examples. 1. Given a = 10, h = 20, A = 106; find the remaining parts. In this case a6, and A 90; therefore the triangle is impossible. 2. Given a = 36, 6 = 80, 1 = 30; find the remaining parts. Here we have 6 sin A = 80 x $ = 40; so that a 6 sin ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ....B' = 180--J3, C" = 180--(A+B')=B--A, a sin C c' =--.--j--Examples. 1. Given a = 10, h = 20, A = 106; find the remaining parts. In this case a6, and A 90; therefore the triangle is impossible. 2. Given a = 36, 6 = 80, 1 = 30; find the remaining parts. Here we have 6 sin A = 80 x $ = 40; so that a 6 sin A, and the triangle is impossible. 3. Given a = 72630, 6 = 117480, = 800'50"; find, C, c. 39. Case III. Given two sides a and b and the included angle C; find the remaining parts, A, B, and c. Solution I. The angles A and B may both be found by means of Formula 27, 35, which may be written tan (4--#=r7 Xta.ni(A+B). Since (A + B) = (180--C), the value of i(A+B) is known; so that this equation enables us to find the value of i (A--B). We then have i(A + B) + i(A-B) = A, and i(A + B)--A--B) = B. After A and B are known, the side c may be found by the Law of Sines, which gives its value in two ways, as follows: a sin C b sin C c =----T or c =--: ----sinl sini? Solution II. The third side c may be found directly from the equation ( 34) c = V a2 + b2--2a cos C; and then, by the Law of Sines, the following equations for computing the values of the angles A and B are obtained: Solution III. If, in the triangle ABC (Fig. 35), BD is drawn perpendicular to the side AC, then It is not necessary, however, to use both formulas. "When one angle, as A, has been found, the other, B, may be found from the relation A+B+C= 180. When the angles are known, the third side is found by the Law of Sines, as in Solution I. Note. When all three unknown parts are required, Solution I. is the most convenient in practice. When only the third side c is desired, Solution II. may be used to advantage, provided the...
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