. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . ABC when (1) a = 4, 6 = 10 ft., C = 30°. Arts. 10 sq. ft. (2) 6=5, c = 20 inches, A = 60°. sq. in. (3) a = 13, b = 14, c = 15 chains. 84 sq. chains. A T> 1111 4. Prove - = —-| 1 5. Prove r = g-g-in^Bsin^C cos^-A EXAMPLES. 157 6. Prove that the area of the triangle ABC is representedby each of the three expressions: 2 R2 sin A sin B sin C, rs, and Br (sin A + sin B + sin C). 7. If A = 60°, a = V3, 6 = V2, prove that the area= i(3+V3). 8. Prove E (sin A + sin B + sin
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . ABC when (1) a = 4, 6 = 10 ft., C = 30°. Arts. 10 sq. ft. (2) 6=5, c = 20 inches, A = 60°. sq. in. (3) a = 13, b = 14, c = 15 chains. 84 sq. chains. A T> 1111 4. Prove - = —-| 1 5. Prove r = g-g-in^Bsin^C cos^-A EXAMPLES. 157 6. Prove that the area of the triangle ABC is representedby each of the three expressions: 2 R2 sin A sin B sin C, rs, and Br (sin A + sin B + sin C). 7. If A = 60°, a = V3, 6 = V2, prove that the area= i(3+V3). 8. Prove E (sin A + sin B + sin C) = s. 9. Prove that the bisectors of the angles A, B, C, of atriangle are, respectively, equal to A B 2 be cos — 2 ea cos — 2ab cos C b + e e + a a + b 106. To find the Area of a Cyclic *Quadrilateral. Let ABCD be the quadrilateral, anda, b, c, and d its sides. Join BD. -Then, area of figure == S = ±ad sin A + \ be sin C= |(ad + 6c)sinA ... (1)NowinAABD, BD2 = a2 + d2- 2adcos A,and in A CBD, BD2 = b2 + c2 - 2 be cos C = &2 + c8-2&ccosA. «™ a a2-62-c2 + d2 . \ cos A = — ?— • 2 (ad + be). sin A =v-[- _ y _ *- i-,vs\ a —6 taa£(A — B) I feiA-^*=*M»=2> (Art v \ \ \ l€ gg - - \ «... — H—(* —- 8. AroaofA=x i*-*)(«-t) EZAMPL1 159 9. Area of A = Ua + h + c) = , .... (Ait. 102)0. r = J(* -°)(-&)(*-T) 11- B = f| (Art. 108) EXAMPLES. Iii a right triangle ABC, in which C is the right angle,prove; the following: i. cos2r. = srA-sl,|2|:. sin-A -f sin-1J 2. sm-,! = r-«2 2c 4. cos*— = 2 2c5. Bin(A-B) + cos2A = a 0. = tan a + b 2 7. siii(A-I!) + sin(2A + C) = 0. 8. tanlA=-^-. & + c 9. (sin A - sin B)*+ (cos A + cos B)1 = 2. 10 ^ja + & i /a —6_ 2sinA ra + 6 Vcos2BIn any triangle ABC, prove the following statements: 11. (a + 6)8in? = ceo8—~—•?2 2 16012. 15. 16. PLANE TRIGONOMETRY. t% \ A • B-C (o — c)
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
