## Elements of Plane Trigonometry |

### From inside the book

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Page 51

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**triangle ABC**, all the triangles so formed will have their angles equal , but the triangles may have their sides D 2 TRIGONOMETRY . 51 1 ... Page 52

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**triangle ABC**, let fall the perpendicular CD , then , by the definitions , CD - AC sin A , and CD CB sin B , C D с B dividing the former by the latter , we have sin A CD CB sin B AC CD = CB ; AC i.e. sin A sin B :: CB : AC :: a : b . In ... Page 59

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**triangle**, and , if it fall between these limits , there is an ambiguity , for there will be two**triangles**having the same data ; thus when the least side AC is opposite the given**triangle**B , it is evident that either**ABC**or**ABC**may ... Page 60

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**triangle**and the sides . By the 20th prop . of the third book of Euclid , the angle AOB is double the angle ACB ...**abc**• = 204 2 2 OA 4R ' We may now find the radius of the circumscribing circle in terms of the sides ; for since ... Page 62

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**triangle**, and p the per- pendicular from one of the equal angles upon the opposite pc side shew that the area = : 4 ...**ABC**prove that - sin ( A sin C B ) = a2 - b2 c2 sin ( A — B ) sin C = sin 62 TRIGONOMETRY .### Other editions - View all

### Common terms and phrases

1+tan AB² AC² angle ACB AP AP AP AP² ARITHMETIC Asin Atan B+cot centre circular measure circumference cos² cos³ cosec cosine cot 4+cot cot A cot cot² OCA diameter distance equal equation Euclid feet Find the number formula given GRAMMAR height Hence hexagon inscribed circle IVY LANE J. R. Young King's College School log blog logarithms nth root number of degrees number of sides perimeter perpendicular plane triangle quadrant radii radius ratio regular polygon Rudimentary Treatise sec² shew sin A cos sin A sin sin¹ sin2 sin² 18 sin³ sine and cosine square subtend subtracted T. H. L. Leary tan-¹ tan² tangent triangle ABC Trigonometry unity VIRTUE BROTHERS W. D. Hamilton

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