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gRIGONOMETRLC FORMULA <br />I. �k.. )a t <br />RightTriangle Oblique TriarlesZ. <br />; <br />b: <br />i of Right Triangles <br />�. 4 a b a, b el <br />For Angle A. ein.= —, cos= , tan= , cot — sec = ,cosec = — <br />3 $ c a b. a b a <br />t Given Required a z , <br />a. b •. ' A; B ,c tan A = b — cotB. a = gZ �- z = a ; } Y 9 <br />a <br />a. a A, B, b ein A = a <br />• ' t 3 — cos B, <br />A, a B,} B=90 --A, b-= a'cotA <br />s.��tl,� . ' _ fi t�, -_ - # r I ! y S '•" Y' sl[3_ A. <br />a�' a B=90 —A, a —' titan A c= b <br />1'✓ w ©v <br />IT j tit, j5i 4: cos A. <br />ll1 r , ' •/� / / + A a _ 'B a 3 B'=$0°. A; a- o ain'11; 4= c coq g, <br />i,. <br />Triangles <br />a Giveu Required a sig B <br />_ a sin C <br />%i-: _• �.+A; B a .a b b — . C = 180"—(�.+ B), <br />4 t• i ; . l — sin .A I i — sin A <br />y f bein A a sin C <br />.4, a b f1,c C BSnB= .a= 180°—(A { B);c — <br />simA <br />a; b, C; 'A tt, c A+B=180°— C, tea }(A—B)-(a-b) tan (A+B)' <br />sin. C <br />sin A <br />�f'ttb ( ;Ji —a+b+e 8_. 8— <br />�a' A,eixi A— <br />S 'j7 Oji i h' a' El D� J �; I y}} }!y,. 2' ..'be <br />I fs ° J 5 <br />stnllB—-180 A B <br />b, c' Area}'a(a--a s— s—c) <br />2 <br />a ; <br />14 �'A; b, c Areal �( area = b a esu r : i <br />i5s� r a' sin B sin Q ' <br />0,- Area ' j lei C ._ <br />2 sin A' j <br />REDUCTION TO HORIZONTAL <br />Horizontal distance= Slope distance multipIied by the f r <br />cosine of the vertical angle. Thus: slope distance=319.4 ft <br />Vert. angle=5 10. From Table, Page 1X. ccs 501(y= <br />o f { 11 m 9959. Horizontal distance' 319.4X.9959=318.09 ft , . <br />lope <br />s Horizontal distance. also =Slope distance minus s <br />)))_ �Se distance times (i—osine of vertical angle), With the <br />' -; same figures as in the preceding example, the follow- <br />G� 0 a i jfz 7 - Horizontal distance ine result is obtained. Cosine 5° 19'=.8959.1—,9959=.0041. <br />�' q„ 519:4X.0041=1.3t: 519.4-1.31=318 09 tt• <br />I When tbe•rise ,is known, the horizontal distance is approximates i <br />9:—theslopedist- <br />anee less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.. i <br />14 14 _ <br />elo distance 3028}i# Horizontal distance=3028---- <br />- i a t- 3X802 8 <br />302.8-0.32=302.28 ft. R <br />i J <br />MADE I% U. 6:A. <br />