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<br />r ��•s r `.L ` TRIGONOMETRIC- FORMUL1E
<br />!t. ✓` �r_, ✓ �f�� ? ter` c 'fir a c a c a
<br />Right Tria*tgle Oblique Triangles
<br />� Soltition of Right Triangles.-
<br />For Angle A. ,sin = e ,cos= a tan= h ,cot = a ,sec = b, cosec = a
<br />'�•.j ^'_._----- F - '.e::.: � A �,��. � .S iF � Given Required � a• _
<br />a, b 1j B ,c tan A B, c
<br />— b =cot
<br />a c d' J3 b
<br />sin A a a:
<br />= c = cos B, b = � (c -f-a) (c—a) = c �I 1— a
<br />;A, a B; b, c B=90°—A, b = acotA,c=sin A.
<br />ra
<br />A, b B, a, c B = 90°—A, a = b tan A, c — cos A.
<br />A, c B, a, b . B=90'—A, a = c sin A., b = c cos A,
<br />-�• ;' js 3� `L' • ^ t rSolution of Oblique Triangles
<br />Given Required
<br />a sin Ba sin C
<br />A, B,a .b, c, C b= sin A'C=1810°—(A {-B),c= sin
<br />b sin A, a sin C
<br /><,
<br />A,a,b B,.c,C sing= a G=180—(A { B),c= sin
<br />0 d a, b, C A, B, c A+B=180°-0, tan (A—B)= a—b) tan z (4+B)
<br />7• r I V 1��� a+
<br />/j/ cy / j h G Jf� J� It G s n A sin -I
<br />C
<br />c i !O7 a+b+c ts-
<br />a b, c .9; B, C s= 2 ,sin'A=-,
<br />z i I be
<br />),C=1S0°—(A+B)
<br />31
<br />�` • — _• -� r a, b, c. Area s= +2+ ,area = 1/s (s—a)((s—b) (s—c)
<br />b c sin A
<br />:A, b, c Area area.= 2
<br />a'sin Bsin C
<br />A, B, C, a Area area =
<br />• _ 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />« pg Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 fL
<br />e S�g�QOce 99 9. Horizontal d istance-319.4Vert. angle � VlCr. From X.9 9e 318.09 ft.IX. cos 5o ld
<br />�.
<br />S,vc�, P��,e distance timesal t(hccosine ofe also lvertcal angle). istance tWiilrlthe
<br />same figures as in the preceding example, the follow-
<br />$ Horizontal distance ing result is obtained. Cosine 5'l0'=.9959.1—.9959= -0Y41-
<br />rr 1 319.4X.0041=1.31.319.4-1.31-318.09 ft.
<br />• j < <� jam, When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />lance less the square of the rise divided by twice the slope distance: Thus: rise=1412.,
<br />r, rr 'slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =302 6-0.32=30°•23 ft.
<br />_ 2 X 3026
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