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<br />�j TRIGONOMETRIC FORMULA;
<br />. 6
<br />a c a. ° a
<br />b r C A�b C A G
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<br />Bight Triangle Oblique Triangles -J
<br />Solution of Right Triangles
<br />;For Angle A. sin = , coo= 8 , tan= a ,cot = b ,sec = �, cosec =
<br />b a b a
<br />Cliven Required 7-- 2
<br />a,b _A,B,c tan A=b= cot B,c=-\/az+ 2=a` + s
<br />_ a
<br />S a, 'c A, B, b sin A = c = cos B, b = v (c a (c -a) = c I =
<br />03
<br />A a- B b e B=90°—A, b= a'@otA, c= a
<br />sin A.
<br />A, b 'B, a, c B = 90°—A, a = b tan A., c = b
<br />' cog
<br />A, _ -
<br />:' A, c B, a, b I B-90*- A, a = c sin A, b = e. cos A,
<br />Solution of Oblique Triangles ,, - .
<br />i a Glv en Required
<br />B,a 'b, e,. C . b=aeinB C=180°-(A+B),c-asinC
<br />' ain A ' sin A
<br />a, -b B, c, C sin B = b sin Ar C = 180°—(A + B), c = a sin C
<br />a sin A
<br />a, b, C A; B, c A+B=180°- C, tan j (A -B)= (a -b) tan 11(A+B)
<br />ab
<br />s c _ a sin C +
<br />x cin A
<br />a, b, c A, B, C s-a+Z+c,sin '4A=.11(s- b(G
<br />sin JB=(')
<br />• Y a c
<br />a+b+o
<br />l` a, b, a _Area s- 2
<br />A, b, e. Area area = h' a sin A q ry
<br />2
<br />A, B, C, a Area ' area = a^ sin B sin C
<br />2sin A ,
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />vsta�ca Vert. angle= 50 10/. From Table, Page IX. cos 511tY=
<br />OC 3 % 9839. Horizontal distance=318.4X.9959=318.09 ft.
<br />O ppgle a Horizontal distance also -Slope distance minus slope
<br />�e distance times (1 -cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 5° 101=.8959. 1-.8859=.0041.
<br />318.4X.0041=1.11. 319.4-1.31=318.09 It.
<br />6 When the rise is known, the horizontal distance is approximately: -the slope dist-
<br />It ce less the square of the rise divided by twice the slope distance. Thug: rise=14 ft.,
<br />slope dtstance=302.0 ft. Horizontal distance=302.5- 14 X 14 =3020 -d_�fL
<br />2X3029
<br />MAGE IN U, S. A.
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