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TRIGONOMETRIC FORMUL&
<br />tI
<br />i3 B B
<br />4 ° a ° a c a
<br />g' b b, C A b C
<br />C
<br />I Right Triangle Oblique 'Triangles
<br />Solution of Right -Triangles
<br />For Angle'A, sin = , cos = , tan = b , cot = a , sec = b , cosec =
<br />Given Required a 2
<br />a, b A,. B ,c tan A = b = cot B, c = -} a2 a = a 1 + r
<br />a, c' A, B, b sinal = a =cosB, b= c a c—a as
<br />02
<br />a B, b, c B=90°—A; b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B=90°—A,a = btanA, c= b
<br />cos A.
<br />A, e, B, a, b B = 90°—A, a = e sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin Ba sin C
<br />4, B, a b, c, C b = sin A ' C = 1800—(A + B), c = sin A
<br />b sin Aa in C
<br />A, a, b B, c, C ' sin B = - a , C = 180°—(A + B), c = sin
<br />a, b, C A, B, c A+B=1800— C, tan i (A—B)= (a—b) tan -.i-. (A+B)�
<br />a F b
<br />a sin C
<br />sin A
<br />a+b+c
<br />a, b, c A, B, C s= 2 ,sinlA= be '
<br />—a)(s—c
<br />—
<br />sin zB=� sC=180°(A+B)
<br />ac
<br />a+b+
<br />c Area s= 2 , area =s(s—a) s— ) (s—c
<br />` A, b, c Area area = b e sin A
<br />a' sin B sin C
<br />B, C, a Area . area = 2' sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />i
<br />ce cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />NoVert. angle= 50 101. From Table, Page IX. cos 50 101=
<br />qo ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />S�0O An��e a Horizontal distance also=Slope distance minus slope
<br />( Ve �. 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:—the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: ,rise=l4 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =3026-0.32=302.28 ft.
<br />2 X 3026
<br />WADE IN
<br />i
<br />t
<br />TRIGONOMETRIC FORMUL&
<br />tI
<br />i3 B B
<br />4 ° a ° a c a
<br />g' b b, C A b C
<br />C
<br />I Right Triangle Oblique 'Triangles
<br />Solution of Right -Triangles
<br />For Angle'A, sin = , cos = , tan = b , cot = a , sec = b , cosec =
<br />Given Required a 2
<br />a, b A,. B ,c tan A = b = cot B, c = -} a2 a = a 1 + r
<br />a, c' A, B, b sinal = a =cosB, b= c a c—a as
<br />02
<br />a B, b, c B=90°—A; b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B=90°—A,a = btanA, c= b
<br />cos A.
<br />A, e, B, a, b B = 90°—A, a = e sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin Ba sin C
<br />4, B, a b, c, C b = sin A ' C = 1800—(A + B), c = sin A
<br />b sin Aa in C
<br />A, a, b B, c, C ' sin B = - a , C = 180°—(A + B), c = sin
<br />a, b, C A, B, c A+B=1800— C, tan i (A—B)= (a—b) tan -.i-. (A+B)�
<br />a F b
<br />a sin C
<br />sin A
<br />a+b+c
<br />a, b, c A, B, C s= 2 ,sinlA= be '
<br />—a)(s—c
<br />—
<br />sin zB=� sC=180°(A+B)
<br />ac
<br />a+b+
<br />c Area s= 2 , area =s(s—a) s— ) (s—c
<br />` A, b, c Area area = b e sin A
<br />a' sin B sin C
<br />B, C, a Area . area = 2' sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />i
<br />ce cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />NoVert. angle= 50 101. From Table, Page IX. cos 50 101=
<br />qo ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />S�0O An��e a Horizontal distance also=Slope distance minus slope
<br />( Ve �. 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:—the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: ,rise=l4 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =3026-0.32=302.28 ft.
<br />2 X 3026
<br />WADE IN
<br />i
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