Given Cafe 4, Ambiguous. One Leg, as AC 28 03 and an Oppofite Angle B = 42 34 1. To find the Hypothenufe B C. The Analogy, SB: SAC:: Rs BC. Make the S of 28° 30', a = S of 42° 34'; fo fhall the = R give the || S of 44° 52', the Quantity of BC. 2. To find the Leg BA. The Analogy, t B: t AC :: R:s B A. Make the T of 28° 30', a = T of 42° 34'; then will the R be the S of 36° 15', for the Leg BA. 3. To find the Angle C. The Analogy, csCA: R::cs B: s C. Make the S of 47° 26', a = S of 61° 30′; fo R give the S of 56° 57', the Quantity will the 1. To find the Hypothenfe B C. The Analogy, R:csCA::cs BA: cs BC. Make the || S of 61° 30′, a = Radius; fo will the S of 53° 45′ be the || S of 45 08', the Complement of B C. VOL. II. S 2. To 2. To find the Angle B. The Analogy, sBA: R::t CA: t B. Make the T of 28° 30′, a = S of 36° 15′; fo will the R be the || T of 42° 34', the Meafure of B. 3. To find the Angle C. The Analogy, CA: RtBA: 1 C. Make the | T of 36o 15′, a = S of 28° 30'; then will the R be the IT of 56° 57', the Measure of 1. To find the Hypothenufe B C. The Analogy, tC: ctB:: Rcs BC. For the Sector, thus, t B: R::ct Ccs BC. Make the T of 33o 03′, a = T of 42° 34′; sọ will = R be the || S of 45 08', the Complement of the Leg B C. 2. To find the Leg B A. The Analogy, SB: csC:: R:cs BA Make the S of 33° 03', a = S of 42° 34′; then will the R be the S of 53° 45, the Complement H of the Leg B A. the 3. To find the other Leg A C. The Analogy, SC: csB:: R: cs AC. Make || S of 47° 26', a = S of 56° 57; fo will R be the S of 61° 30', the Complement of the Leg AC. CHA P. XIII. The fifth Method of folving Right-angled Spherical Triangles, by the Sliding Rule. T HE Nature and Ufe of the Sliding Rule alfo, has been already fufficiently explained in Vol. 1. of Plain Trigonometry; however as its Ufe is here fomewhat different; I fhall just give Examples of all the real Cafes of a Right-angled Spherical Triangle this way; in order to underftand the Method of operating by this moft convenient Inftrument, I fhall again acquaint the Reader, that, as it confifts of two Parts, the Fixed and the Moveable or Sliding Part, and each of thefe hath a Line of Sines and Tangents, fo placed as that the Sines on the Slider move by the Sines on the fixed Part, and the fame of the Tangents; I fhall (in the Sequel) mark the Line of Sines and Tangents on the Rule (or fixed Part) by the Letter F, and those on the Slider by the Letter I; this being premifed, and the Reader prefuppofed to understand the Nature of VOL. II. S 2 the the Sines on the Rule; I fhall proceed to the Solution of the Six Cafes as before, with all their Varieties, by this Inftrument. Cafe 1. The Hypothenuse BC 44 52 Given and an Oblique Angle, as C = 56 57 1. To find the Leg B A. The Analogy, R: s C :: s B C : s B A. Set the Sine of 90° on F, to the Sine of 56° 57' on L; then against the Sine of 44° 52′ on F, is the Sine of 369 15′ on L. 2. To find the other Leg A C. The Analogy, RtBC::cs C: t AC. Set the Sine of 90° on F, to the Sine of 33° 03' on L; then against the Tangent of 44° 52' on F, is the Tangent of 28o 30' on L. 3. To find the Angle B. The Analogy, RcsBC: tC c t B. Set the Sine of 90o on F, to the Sine of 45 08! on L; then against the Tangent of 56° 57′ on L, is the Tangent of 47° 26' on F. But the Tangent and Cotangent are in the fame Point on the Line; fo that in the fame Place you alfo fee 42° 34' = B required. Cafe 2. Given { The Hypothenuse BC 44 52 and one of the Legs, as B A = 36 15 1. To find the other Leg A C. The Analogy, csBA: R:: csBC: cs AC. Set the Sine of 53° 45' on F, to the Sine of 90° on L; then against the Sine of 45o 08' on F, is the Sine of 61° 30' on L. 1 2. To find the Angle B. The Analogy, tBC: R::tBA: cs B. Set the T of 44° 524 on F, to the T of 368 15 on L; then against the S of 90% on F, is the S of 47° 26' on L. 3. To find the Angle C. The Analogy, s BC: Set the S of 44° 52′ on F, then against the S of 369 15' 56° 57' on L. R::s B A: s C. 1. To find the Hypothenufe B C. The Analogy, R: csB: ct AB: ct BC. Set the S of 90% on F, to the S of 47° 26' on L; then against the T of 539 45 on L, is the T 45 08 of 44 52 2} on F. |
