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TRIGONOMETRIC FORMULAE
<br />a a a
<br />•� ��02 . Fncr
<br />3,9, 60 3 776 i fe-„ct ' Fx T is f' D$ % ` Righ b Triangle C Oblique Triangles
<br />All Solution of Right Triangles
<br />/ a
<br />3 y �,J /-�nCc Co> ; ' z�6? - For Angle A. 'sin = a , cos = b , tan = ¢ , cot = b , sec = , cosec = c
<br />t Given Required
<br />�rrrc^C /� a, b .ti,'B ,c tan A = b = cot B, c = az + s = a 1 + a�
<br />5� k S X55
<br />e 62
<br />._:_.----, -- a as
<br />a.: c A� B, b sin A = — = cos B, b =.� (a+a),(c—a) 1— —
<br />'./•4 / 24,
<br />A, a IB; = "b, c B=90°—A, b acotA,�= a
<br />�;=�,.._ " •;..- �<t ..�" -stn d
<br />_ R 7 A; b B, a, c B= 90 s A, a b tan A; c x b
<br />%y
<br />t�
<br />A, c; =B, a b B, 90° -A'; -a ostA,;b c cos A; .
<br />{ i w Soiutron of;- Oblique Triangles '
<br />Given - Required ra stn B ' S ;k ds sinC
<br />e r
<br />A' �' a b' sin A ' . I B) : e :. .
<br />bsinA sin
<br />A, a; b 1B, a,' (; sin B = , C = 180°=(A -1- B); u = a sin C
<br />a, b, C A , B c ten s GAS B)- (a—b} L'an '-z (A+ B)
<br />azsiII ri
<br />6fT i-' s c sin A
<br />E ' q
<br />s-6 ��3 ai �. t a, b, c A, B C s— 2 ,sin zA—N b c '
<br />z1 s—a�(� Lv=1,80 A+B)
<br />IB-- I °-(
<br />1 i b, c :Area, s= 2 ,area
<br />_
<br />3 _ . ble sin A,:
<br />A' b' c r Area , area
<br />as sin B sin 6--
<br />B, C, m Area - area = 2 sinA
<br />_J t' REDUCTION TO- HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope elastance =319.4 ft.
<br />Vert. anle= 50 101. Fro' I r Qe a�s�snee d 9959. Horizontal distance 19.4X. 9 3 8.09 ftTable, Page JX. cos5° ld
<br />.S% e =1 Horizontal distance -also = Slope distance minus slope
<br />" qe a distance times (1—cosine of vertical a-mgle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 5° 1o'=.99 .1—.959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />!' When the rise is known, the horizontal distance is approximateI!r the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise =14 ft,
<br />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =3016-40.32=302.28 ft.
<br />2 X 3026
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