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<br />TRIGONOMETRIC FORMUL,,Eu--_.:_ — 4
<br />B B B
<br />zc a ° a ° a
<br />Ott ' A A
<br />b C b G' G A C
<br />Right Triangle Oblique Triangles
<br />? Solution of Right Triangles
<br />a b a b c c
<br />For Angle A. sin = c , cos + c , tan= b , cot = a , sec = �, cosec = a
<br />Given Required a
<br />z
<br />1
<br />a,b A,B,c tan A=b=cotB,c=voT-Y,=a 1+ a!
<br />• . a -
<br />a, c A, B, b sin A = o = cos B, b = \/ (c+a) (c—a) =c 1—as s
<br />0
<br />l A, a B, b, c B= 90'—A, b= a cot A, c= a
<br />sin A.
<br />b
<br />a c B= 90°—A, a= b tan A, e=
<br />cos A.
<br />A, c B, a, 'b B=90°—A, a = csinA, b= e cos A,
<br />JSolution of Oblique Triangles
<br />Given Required. a sin Ba sin C
<br />A, B; a-• _b,. c, C b = sin A ' C = 180°—(A + B), c = sin A
<br />b sin A a sin C -
<br />A, a, b B, c, C sin B = a , C = 180°—(A -I- B), c = sin A
<br />a, b,, C. .4, B, c A+B=180'— C, tan' (A—B)= (a—b) tan' (A+B)
<br />a sin C
<br />c=
<br />sin A
<br />a, b, cJ A,B,C s=a+2+c,sin'A—.(c—c
<br />sin�B= AI(,—a)(- ` , C=180'—(A+B)
<br />i'a, b, c Area s=a+2+c> area., =.1 s(s—a s—')(s—c)-
<br />C'j ,
<br />A, b, c' -Area area = b c sin °_ yy,32.
<br />a= sin B sin 0 5,19
<br />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 =310.4 ft.
<br />t3o°c Vert. angle= 50 101. From Table, Page IX. cos 50 lot=
<br />e ass N 9959. Horizontal distance=319.4X.9959=318.09 ft
<br />5%op' tie Horizontal distance also=Slane distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />ing result is obtained. Cosine 5°101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=818.09 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=14 ft.,
<br />—
<br />slope distance=302.0 ft horizontal distance=3026— 14 X 14 —3026-0.32=80228Yt.
<br />2 X 802.6
<br />/ NADA IN Ut6sA.
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<br />B B B
<br />zc a ° a ° a
<br />Ott ' A A
<br />b C b G' G A C
<br />Right Triangle Oblique Triangles
<br />? Solution of Right Triangles
<br />a b a b c c
<br />For Angle A. sin = c , cos + c , tan= b , cot = a , sec = �, cosec = a
<br />Given Required a
<br />z
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<br />a,b A,B,c tan A=b=cotB,c=voT-Y,=a 1+ a!
<br />• . a -
<br />a, c A, B, b sin A = o = cos B, b = \/ (c+a) (c—a) =c 1—as s
<br />0
<br />l A, a B, b, c B= 90'—A, b= a cot A, c= a
<br />sin A.
<br />b
<br />a c B= 90°—A, a= b tan A, e=
<br />cos A.
<br />A, c B, a, 'b B=90°—A, a = csinA, b= e cos A,
<br />JSolution of Oblique Triangles
<br />Given Required. a sin Ba sin C
<br />A, B; a-• _b,. c, C b = sin A ' C = 180°—(A + B), c = sin A
<br />b sin A a sin C -
<br />A, a, b B, c, C sin B = a , C = 180°—(A -I- B), c = sin A
<br />a, b,, C. .4, B, c A+B=180'— C, tan' (A—B)= (a—b) tan' (A+B)
<br />a sin C
<br />c=
<br />sin A
<br />a, b, cJ A,B,C s=a+2+c,sin'A—.(c—c
<br />sin�B= AI(,—a)(- ` , C=180'—(A+B)
<br />i'a, b, c Area s=a+2+c> area., =.1 s(s—a s—')(s—c)-
<br />C'j ,
<br />A, b, c' -Area area = b c sin °_ yy,32.
<br />a= sin B sin 0 5,19
<br />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 =310.4 ft.
<br />t3o°c Vert. angle= 50 101. From Table, Page IX. cos 50 lot=
<br />e ass N 9959. Horizontal distance=319.4X.9959=318.09 ft
<br />5%op' tie Horizontal distance also=Slane distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />ing result is obtained. Cosine 5°101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=818.09 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=14 ft.,
<br />—
<br />slope distance=302.0 ft horizontal distance=3026— 14 X 14 —3026-0.32=80228Yt.
<br />2 X 802.6
<br />/ NADA IN Ut6sA.
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