The book New Plane And Spherical Trigonometry was written by author Webster Wells Here you can read free online of New Plane And Spherical Trigonometry book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is New Plane And Spherical Trigonometry a good or bad book?
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7. Given A = 78^ 42' 53", b = .0520281. 8. Given a = .932368, c = 4.786723. 9. Given 5 = 72^8' 27", c = 27.28338. 10. Given J5 = 49* 25' 34", &=. 3376494. Digitized by Google PLANE TRIGONOMETRY. Vn. QENERAL PROPERTIES OF TRIANQLEa ]j07. In any triangle, the mdes are proportional to the wms of theif egpoaUe angles. L Topiove a:6 = 8injl:8m& (47) There will be two cases, according as the angles A and B are both acute (Fig. 1), or one of them obtuse (Fig. 2). In each case, draw CD perpendicular to... AB. Then in each figure, CD = & sin^l (§ 4). Also in Fig. 1, CD=^a sin B. And in Fig. 2, CD=ra sin CBD = a sin (180** — S) = a sin^ ($ 38). & sin jii = a sin B. Then in either case. Whence by the theory of proportion, a: &=:sinj!i: sinJ3. In like manner, 5 : o = sin B : sin C, and o: as sin C7: sin A (48) (49) 106L In any triangle, the gum of any two aides is to their difference as thetangent of half the sum of the opposite angles is to the tangent of half their .difference. By (47), a:& = sinj!i:sinA Whence by composition and division, a + &:a — & = sin jii + sin^: sin jl — Bin& a + b sin jii + sin JB Or.