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<br />TRIGONOMETRIC FORMULAE
<br />B B B
<br />c a c a c' a
<br />l g b C Afb C A b C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a_ b a b c c
<br />t. For Angle A, sin a , cos = a , tan = b , cot = a —,sec= b , cosec = —
<br />a
<br />Given Required
<br />a,b A,B,c 'tan A=b=cotB,c= az+ s=a 1 +32
<br />)" a, c A, B, b sin A = o = cos B, b = %/ (c+a) (c—a) = c 1— o
<br />A, a B, b, c B = 90°—A, b = a cot A, c.= a
<br />sin A':
<br />A, b B, a, c B=90°—A,a =.b tan A, c= b
<br />cos A.
<br />A, c B, a, b B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin B
<br />A, B, a b, c, C b' = in A , C = 180°—(A .+ B), a = s "in A
<br />A, a, b B, c, C ein B = b sin A a sin C
<br />a , C = 180°—(A + B), c = sin A
<br />a, b, C A, B, c A+B=180°— C, tan 3 (A—B)= (a—b) tan 's (A+B) .
<br />j a -sin C a+b
<br />c = sin A
<br />a, b, c A, B, C e=a+2+a,,in 'A=`I s G),
<br />Bing —\ s a(c ) C=1800=(A+B)
<br />a+b+e,
<br />a, b, c Area s= 2
<br />A; b, c Area area •_ basin A
<br />2
<br />az sin B sin C
<br />1 A, B, C, a Area area = 2 sin 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 />astaope Vert angle= 50 101. From Table, Page IX. cos 50 101=
<br />9959. Horizontal distance=319.4X.9959=318.09 ft
<br />So c, Arg1e = Horizontal distance also=Slone distance minus slope
<br />Ve t. a 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 50 101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—tbe 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=3026— 14 X 14 _3n6-0.32=302.28 ft
<br />2 X 3026
<br />MADE IN U."S. A.
<br />.I
<br />l�
<br />TRIGONOMETRIC FORMULAE
<br />B B B
<br />c a c a c' a
<br />l g b C Afb C A b C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a_ b a b c c
<br />t. For Angle A, sin a , cos = a , tan = b , cot = a —,sec= b , cosec = —
<br />a
<br />Given Required
<br />a,b A,B,c 'tan A=b=cotB,c= az+ s=a 1 +32
<br />)" a, c A, B, b sin A = o = cos B, b = %/ (c+a) (c—a) = c 1— o
<br />A, a B, b, c B = 90°—A, b = a cot A, c.= a
<br />sin A':
<br />A, b B, a, c B=90°—A,a =.b tan A, c= b
<br />cos A.
<br />A, c B, a, b B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin B
<br />A, B, a b, c, C b' = in A , C = 180°—(A .+ B), a = s "in A
<br />A, a, b B, c, C ein B = b sin A a sin C
<br />a , C = 180°—(A + B), c = sin A
<br />a, b, C A, B, c A+B=180°— C, tan 3 (A—B)= (a—b) tan 's (A+B) .
<br />j a -sin C a+b
<br />c = sin A
<br />a, b, c A, B, C e=a+2+a,,in 'A=`I s G),
<br />Bing —\ s a(c ) C=1800=(A+B)
<br />a+b+e,
<br />a, b, c Area s= 2
<br />A; b, c Area area •_ basin A
<br />2
<br />az sin B sin C
<br />1 A, B, C, a Area area = 2 sin 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 />astaope Vert angle= 50 101. From Table, Page IX. cos 50 101=
<br />9959. Horizontal distance=319.4X.9959=318.09 ft
<br />So c, Arg1e = Horizontal distance also=Slone distance minus slope
<br />Ve t. a 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 50 101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—tbe 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=3026— 14 X 14 _3n6-0.32=302.28 ft
<br />2 X 3026
<br />MADE IN U."S. A.
<br />.I
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